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ECLECTIC EDUCATIONAL SERIES. 



THE 



ELEMENTS OF PHYSICS 



A TEXT-BOOK FOR 



ACADEMIES AND COMMON SCHOOLS 



SIDNEY A. NORTON, A. M. 



VAN ANTWERP, BRAGG & CO., 

[37 Walnut Street, 2 8 Bon d Str eet, 

CINCINNATI. NEW YORK. 



leys 



COPYRIGHT, 1875, BY WILSON, HINKLE & CO. 




if, /fid 



t 



ECLECTIC PRESS! 

VAN ANTWERP, BRAGG & CO., 

CINCINNATI. 



PREFACE. 



This volume has been prepared, at the request of many 
teachers, for the use of pupils in academies and common 
schools. The topics considered have been selected with ref- 
erence both to the average age of such pupils and to the 
time usually allotted to the study . of Physics. 

The object of this book is not merely to give a system- 
atic and symmetrical epitome of the Science, but so to pre- 
sent each topic that the pupil shall receive, from the first, 
clear, accurate, and scientific ideas. In no other way can 
the study of any science be made a means of mental dis- 
cipline. No pains have been spared to attain this result; 
and it is hoped that, however much has been omitted that 
many teachers would desire to have presented, the pupil will, 
at least, have nothing to unlearn. 



(iii) 



TABLE OF CONTENTS. 



CHAPTER I. FAOB 

General notions of matter and force 7 

CHAPTER II. 
Phenomena connected with cohesion 27 

CHAPTER III. 
Phenomena connected with adhesion 33 

CHAPTER IV. 
The laws of motion 41 

CHAPTER V. 
Phenomena connected with gravitation 50 

CHAPTER VI. 
The laws of falling bodies 57 

CHAPTER VII. 
The pendulum 65 



vi CONTENTS. 

CHAPTER VIII. 
Simple machines 72 

CHAPTER IX. 

Fluids at rest 91 

CHAPTER X. 
Fluids in motion 103 

CHAPTER XI. 
The phenomena of aeriform fluids 10S 

CHAPTER XII. 
The modes of molecular motion 128 

CHAPTER XIII. 
Acoustics, or the phenomena of sound . . . ... . 135 

CHAPTER XIV. 
Optics, or the phenomena of light 153 

CHAPTER XV. 
The phenomena of heat, or Pyronomics ..... 196 

CHAPTER XVI. 
Electricity 228 



THE 



ELEMENTS OF PHYSIOS. 



CHAPTER I. 

GENERAL NOTIONS OF MATTER AND FORCE. 

1. Matter is any thing that is capable of affecting our 
senses. The objects that surround us, the food we eat, the 
water we drink, the air we breathe, are different forms of 
matter. 

2. A body is any separate portion of matter, whether 
large or small: thus a mountain, a pebble, or a dew-drop, 
is a body. The different materials of which bodies are 
composed are called substances: thus iron, wood, and sugar 
are substances. 

3. Some substances contain but one kind of matter. 
These are called simple substances, or the elements. There are 

I sixty-three elements now known. The most abundant of 
these are oxygen, silicon, aluminium, iron, calcium, mag- 
nesium, sodium, potassium, nitrogen, hydrogen, and carbon. 

4. Compound substances are composed of at least two 
elements, so firmly united that they can not be separated 
except by chemical processes. These compound substances 
make up the bulk of the globe : thus water is composed of 

(7) 



8 ELEMENTS OF PHYSICS. 

oxygen and hydrogen ; quartz and white sand, of silicon and 
oxygen; clay, mainly of silicon, oxygen, and aluminium. 

5. Many bodies are mixtures of several substances : thus 
gunpowder is a mixture of niter, carbon, and sulphur. The 
air is also a mixture. The most important of its constituents 
are oxygen, nitrogen, carbonic acid, and the vapor of water. 

6. Many substances can exist at different times in three 
different states: thus water can exist as ice, as water, or as 
steam. 

A body is in the solid state when its particles are held firmly 
together, and retain the shape that has been given them by 
nature or art. Ice, wood, and tallow are solids. 

A body is in the liquid state when its particles easily change 
their relative positions. When a liquid is poured into an 
open vessel, it adapts itself to the shape of the vessel, except 
that its upper surface is horizontal. Water, alcohol, and oil 
are liquids. 

A body is in the aeriform state when its particles tend to 
separate from each other, and to occupy a greater volume. 
Bodies in this state are called aeriform bodies, gases, or vapors. 
Aeriform bodies can not be retained in an open vessel; and 
when shut in on all sides, completely fill the vessel in which 
they are placed. Steam, the air, and illuminating gas are 
aeriform bodies. 

The term fluid is applied both to liquids and aeriform 
bodies: thus we may speak of water as a liquid or as a fluid; 
or of air as an aeriform body or as fluid. 

7. No one can conceive of a body which does mot possess 
length, breadth, and thickness. Even the fine particles of 
dust which are seen only in the path of the sunbeam must 
have a certain shape or figure, and occupy a certain amount 
of space. The amount of space that a body occupies is 
called its bulk or volume. 



MEASURES. 



9 



The ordinary measures in the United States are derived 
from an arbitrary unit called the yard ; although we may use 
any one of its divisions or multiples as a unit — as the inch, foot, 
or mile. The square inch, square yard, etc., are units of sur- 
face. The cubic inch, cubic foot, etc., are units of volume. 

The wine gallon of the United States contains 231 cubic 
inches. The imperial gallon of England contains 277.274 
cubic inches. 

The French unit of length is the metre, 
which is equal to 39.3685 of our inches. 
All the French measures increase or de- 
crease in decimal proportion. For the 
increase the Greek prefixes deca (10), 
hecto (100), and kilo (1000), are used; 
for the decrease the Latin prefixes deci 
( T V), centi (yfo), and milli fj^), are 
used. A decimetre is drawn in Figure 1, 
in comparison with a scale of inches. 
One inch is very nearly 25.4 millimetres. 

The French unit of volume is a cubic 
decimetre, and is called the litre. It 
contains 61.022 cubic inches, or 2.113 
wine pints. 

8. All bodies may be divided into 
very minute particles: thus stones may 
be crushed to powder; the hardest steel 
may be broken; and even the diamond 
may be reduced to dust. Wonderful ex- 
amples of minute divisibility are afforded 
by odors and coloring matters. Odors 
can be caused only by particles of matter fig. i. 

in the air; and yet how small must those be that enable 
a hound to follow his game ! A grain of musk has perfumed 



10 ELEMENTS OF PHYSICS. 

a large apartment for several years without perceptibly los- 
ing in weight. An ounce of aniline is capable of coloring 
two hundred ounces of silk thread. We may separate this 
thread into 3,000,000,000,000 parts and discern the red color 
of the aniline in each one of them. 

Many chemical tests reveal the presence of exceedingly 
small quantities of matter. If a grain of iron or of copper 
be dissolved in nitric acid, and then added to a tumblerful 
of water, the presence of either metal may be detected in 
every part of the mixture. This may be done by placing a 
drop of the solution on a watch-glass and then adding a solu- 
tion of ferrocyanide of potassium, when the iron solution will 
be turned blue, and the copper solution will be reddened. 

Even by mechanical means we may obtain particles so 
small that it is difficult to form just conceptions of their 
size. Gold leaf is sometime^o thin that fifteen hundred 
leaves placed one above another will not equal the thickness 
of ordinary paper. One square inch of this leaf weighs less 
than one twenty-thousandth part of an ounce ; and we can 
divide this into ten-thousand parts, each one of which is 
distinctly visible to the eye, though weighing less than one 
two-hundred-millionth part of an ounce. 

9. There are many reasons for believing that there is 
a limit to the divisibility of matter. The smallest conceiv- 
able particle of water, or of any compound body, is called a 
molecule. A molecule is so small that no microscope will 
ever enable us to see it. It is the smallest particle into 
which a body may be divided without losing its identity. 

10. By chemical means a molecule of water may be still 
further divided into its components oxygen and hydrogen, 
and thus particles obtained which are the smallest conceiv- 
able. These' are called atoms. An atom is the smallest 
particle of matter capable of entering into a molecule. 



POROSITY. 



11 




Fig. 2. 



11. How the atoms are arranged to form molecules, or 
how the molecules are arranged in bodies, is unknown. We 
know that all bodies expand when heated, and contract when 
cooled.* Thus, if an empty flask is inverted in a vessel of 
water, and heat is applied (Fig. 2), the air will expand so 
much that a portion will be expelled. 
On cooling, the air remaining in the 
flask will resume its original volume. 
We know also that all bodies are made 
smaller by pressure : thus a bottle of 
"soda water" contains several times 
its volume of compressed gas, which 
expands to its original volume when 
the cork is removed. All bodies are 
expansible and compressible. Gases 
show these properties very rjpfcdily, but they are also exhi- 
bited by solids and liquids. 

These and similar phenomena render it probable (1) that 
the molecules of a body do not touch each other, but are sep- 
arated by vacant spaces or pores ; and (2) that the molecules 
are free to move even in the most rigid bodies. When bodies 
expand, the molecules separate, and the pores become larger; 
when bodies contract, the molecules approach, and the pores 
become smaller. 

12. The pores of bodies are of two kinds. (1) Those 
which exist between molecules are called physical pores. These 
are so small that they can not be seen even by the aid of a 
microscope. (2) Sensible pores are cavities that may be seen, 
as the pores in bread, or in some kinds of wood. 

If water is heated in a glass vessel, bubbles of air sep- 



•-When day is heated, it contracts permanently, because its par- 
ticles suffer a chemical change. 



12 ELEMENTS OF PHYSICS. 

arate out and cling for a time to the sides of the vessel. 
These must have come from the physical pores of the water. 
So also, if a cup be filled to the brim with hot water, two 
or three spoonfuls of pulverized sugar may be gradually 
added before the cup overflows. The molecules of the sugar 
find sufficient space in the pores of the water. Sometimes 
an actual contraction of volume occurs on mixing two 
liquids. Thus, if a long and slender test-tube be half filled 
with water, and strong alcohol be poured carefully in, so as 
not to mix the two liquids until the tube is quite filled, and 
then the tube be tightly closed and inverted, the liquids will 
mix and no longer fill the tube. The explanation of this 
phenomenon is that the molecules of the alcohol and the 
water are mutually so arranged as partially to fill the pores 
previously existing in the two bodies. 

13. We do not believe it possible that any two particles 
of matter can occupy the same place at the same time. In 
other words, we believe that matter is impenetrable. If a 
pebble be dropped into a tumblerful of water, enough water 
will overflow to equal the bulk of the pebble. The ex- 
amples given in the preceding section are only apparent 
exceptions to the property of impenetrability. There are 
other apparent exceptions, which can be even more readily 
explained. 

If one end of a glass tube be closed by the thumb, and 
the other end plunged into a vessel of water, the water can 
not fill the tube because of the impenetrability of the air 
inclosed in the tube. Nevertheless it will be seen that the 
water will rise a little way in the tube; but this is because 
the air is compressed, and so allows space for the water to 
enter. 

An easy experiment, which illustrates the same fact, may 
be made by wrapping moistened paper around the tube of a 




DENSITY. 13 

funnel, so that it may be made to fit air-tight in the neck 
of a bottle, as shown in Fig. 3. Now, if water be' 
quickly poured into the funnel, only so much will 
enter the bottle as corresponds to the compressed or 
displaced air. /if 

14. Space which contains no matter is called a 
vacuum. 

15. Bodies vary greatly with respect to the 
pores which they contain. Those that contain FlG - 3 - 
large pores are called rare bodies ; those that have small 
pores are called dense bodies. Density is, therefore, a term 
which expresses the relative amount of matter which equal 
volumes of different substances contain. Iron, for example, 
is denser than stone, but is less dense than gold. In com- 
paring the relative density of bodies, it is convenient to 
select some substance which shall be taken as the standard 
of comparison, and reckoned as unity, or 1. Thus the air 
is a standard of density for all aeriform bodies, and water is 
a standard of density for liquids and solids. It is also nec- 
essary to select some temperature at w T hich the comparison 
shall be made. The temperature usually taken is 32° F. for 
all bodies excepting water, which is unity w T hen at 39°. 2 F. 
In the case of gases, it is also necessary that they should be 

I compared when under the same pressure. The pressure as- 
sumed is the average pressure of the atmosphere at the level 

! of the sea, which is 14.7 pounds to the square inch, and 
which equals a column of mercury 29.92 inches high.* 

i These are called the normal conditions of temperature and 

i pressure. 

16. The ratio which show T s how many times heavier any 
I given substance is than an equal volume of water or of air, 



*See Section 31. 



14 



ELEMENTS OF PHYSICS. 



; 



under the normal conditions, is the specific gravity of the sub- 
stance. The specific gravity of chlorine gas is 2.47, which 
means that a given bulk of chlorine, as a pint or a gallon, is 
2,47 times heavier than the same bulk of air. The specific 
gravity of silver is 10.5, which means that a given bulk of 
silver, as a cubic inch, weighs 10.5 times more than the same 
bulk of w r ater. 

Weights of the Standards. 

One cubic inch of air weighs, at 32° F., 0.32712 grains. 

at 60° F., 0.30954 grains. 
One cubic in. of water weighs, at 32° F., 252.875 grains. 

at 60° F., 252.456 grains. 

Specific Gravities Compared. 

at 32° F. at 62° F. 

Katio of air to water, 1 to 773.2 1 to 816.8 
Katio of water to air, 1 to .00129363 1 to .0012243 



Table of Specific 


Gravities. 




OASES. 




SOLIDS. 




Air, 


1. 


Cork, 


0.24 


Steam, 


.622 


Ice, 


0.93 


Hydrogen, 


.069 


White Oak, 


0.86 


Oxygen, 


1.106 


Ebony, 


1.33 


LIQUIDS. 




Glass, 


3. 


Pure Water, 


1. 


Iron, 


7.78 


Sea Water, 


1.026 


Copper, 


8.85 


Olive Oil, 


0.915 


Lead, 


11.35 


Sulphuric Acid, 


1.84 


Gold, 


19.26 


Saturated Brine, 


1.205 


Platinum, 


21.53 



17. Matter is every- where subject to change. When 
the smith heats a bar of steel, it expands ; when he beats it 
on his anvil, he is changing its form; when he hurls it from 



MOTION. 15 

him, he is changing its position. If the steel be rubbed on 
a magnet, it acquires the property of attracting iron filings. 
It may be melted to a fluid state and cast into any shape. 
Such changes as these are called physical changes. Physical 
changes are those by which the substance is not altered so 
as to lose its identity. 

On the other hand, in chemical changes the identity of the 
substance is entirely lost. Thus, when steel rusts, the red 
powder which forms is due to a chemical change in which 
water has been decomposed into oxygen and hydrogen ; the 
oxygen has united with the iron in the steel, to form a new 
kind of substance, and the hydrogen has escaped into the 
air. So, also, the decay of leaves, the burning of wood, the 
souring of cider, are chemical changes. 

18. Force is that which causes any change in the form 
1 or condition of matter. All the phenomena of the visible 

universe are caused by the action of force upon matter. 

The simplest change in matter is that of position. We 
determine the motion or rest of a body by its relation to 
some given point ; but as this point may be itself fixed or 
moving, motion or rest is either (1) absolute, or (2) relative. 

19. Absolute motion is change of place with regard to a 
i fixed point : relative motion is change of place with regard 
' to a point in motion. 

The motion of the heavenly bodies with reference to ideal 

■' fixed points in space are examples of absolute motion. 

I Strictly speaking, no bodies are in a state of absolute rest. 

I Every particle on the earth's surface partakes of all the daily 

and annual motions of the earth ; and, therefore, the terms 

absolute motion and rest, when applied to bodies on the 

earth's surface, have reference to objects that appear fixed. 

A person seated on a steamboat in motion is in absolute 

motion with respect to the harbor he has left, or to the har- 



16 ELEMENTS OF PHYSICS. 

bor he is approaching, and is in a state of relative rest with 
regard to the parts of the vessel. If he walks toward the 
stern of the boat as fast as the vessel moves forward, he is 
in a state of relative motion with regard to the parts of the * 
vessel, but is in absolute rest with regard to the harbors. 

20. Velocity is the rate of motion. It may be found by 
dividing the space passed over by the time occupied in the 
transit. Thus, if a locomotive is five hours in going one 
hundred miles, its velocity is twenty miles an hour. 

The formula, v = s — r- 1 
Expresses the relation between space, time, and velocity. 

21. A natural unit of time is the day, but any of its 

subdivisions — hour, minute, or second — may be assumed as 
convenience dictates. 



Man walking, 
Man running, 
Swift trotting horse, 
A rifle ball, 
Sound, 



Table of Velocities. 




MILES PER HOUR. 


FEET PER SECOND 


3 


4.4 


10 


14.66 


•se, 27 


40. 


1,000 


1,466.66 


762 


1,117.6 



22. Motion and rest are equally natural to a body. 
When the forces that are acting upon matter exactly balance 
each other, it is at rest, and is in motion when they do not. 
We say, then, that matter has the property of inertia, by 
which we mean that it tends to retain its present state, 
whether of motion or of rest. 

It requires some force to set a body in motion, and when 
it is in motion, it requires force to stop it. The inertia of 
the air becomes manifest by the resistance it offers to a body 
moving through it. If we endeavor to run with an open 
umbrella, we need to employ considerable force to overcome 



FORCES IN NATURE. 17 

the resistance of the air, because we shall have to displace 
or set in motion the air which is in front of us. 

The heavier a body is, the greater will be its inertia ; that 
is, it will require more force than a lighter body to set it in 
motion, or to stop it when it is moving. Thus, a small boy 
will easily "dodge" a larger, because the heavier boy will be 
unable to change his course at once. 

A person standing in a wagon partakes of its condition of 
motion or rest. If it is suddenly set in motion, he is thrown 
backward, because his feet are drawn along by the friction 
against the bottom, before his head can acquire the motion 
forward. If the wagon is suddenly stopped when in rapid 
motion, he is thrown forward. 

23. There are many forces in Nature, and it is conven- 
ient to divide them into three classes. 

(1) Those which act only upon the molecules of matter, 
and at distances which are inappreciable to our senses. These 
are named Cohesion, Adhesion, and Affinity. Taken collect- 
ively, they are called the molecular forces. 

(2) Those which act also upon bodies taken as a whole, 
and at both sensible and insensible distances. These are 
Gravitation, Light, Heat, and Electricity. 

(3) Those which take part in the phenomena of living 
plants. and animals by controlling or modifying the forces of 
inanimate nature. These are called the vital forces. 

24. Cohesion causes like molecules to unite in one mass. 
It keeps the particles of a body together. It is strongly ex- 
erted in solids, feebly in liquids, and not at all in aeriform 
bodies. Thus a dew-drop is spheroidal because of the co- 
hesive force. When the drop is very large it becomes flat- 
tened, because the force of cohesion is partly overcome by 

! the force of gravitation. 

The following pretty experiment illustrates the tendency 

Phys. 2. 



18 ELEMENTS OF PHYSICS. 

of liquids to assume the spheroidal form : Take a wine-glass 
half full of water, and carefully fill it with alcohol so as not 
to mix the two liquids; then drop a very little olive oil 
through the alcohol. It will come to rest in the middle of 
the glass, and, if the quantity taken is not too great, will as- 
sume the shape of a ball. 

When the cohesion of solids has been once destroyed, it is 
difficult to cause the particles to reunite. If a bar of lead 
be cut in two, the severed parts may be made to cohere by 
so cutting their faces that they will present a bright and 
even surface, and then pressing them tightly together with 
a slight twisting motion. Two plates of polished glass will 
cohere, under pressure, so firmly that they may be worked as 
a single piece. 

25. Adhesion causes the molecules of different kinds of 
matter to cling together. Thus, adhesion causes the dust to 
cling to any thing it falls upon ; chalk to cling to black- 
boards, and dew-drops to leaves. Under the name of Friction 
it diminishes the work of moving force, (1) by stiffening the 
joints of machines, (2) by increasing the resistance to be 
overcome. Friction often acts as a mechanical advantage, as 
in retaining nails and screws in their sockets, in preventing 
our feet from slipping when standing or walking, and in en- 
abling us to take firm hold upon objects. 

26. Affinity causes the atoms of unlike substances to 
unite and form new kinds of matter. All chemical phe- 
nomena are due to affinity. When iron dissolves in nitric 
acid a new kind of matter (the nitrate of iron), differing 
both from the iron and the acid, is formed. 

Adhesion and cohesion differ from affinity in this, that 
their action on bodies does not effect any essential change in 
the properties of the bodies acted upon. They differ from 
each other in this, that adhesion acts between unlike par- 



GRAVITATION. 19 

tides, and cohesion between like particles. They all agree in 
this, that their energy increases with the number of mole- 
cules that are acted upon. This statement, when applied to 
solids, may be expressed in these words : the energy of 
molecular forces increases with the extent of surface exposed 
to their action. 

27. Gravitation is a force by virtue of which every par- 
ticle of matter attracts every other particle of matter toward 
itself. The term mass is used to denote the amount of matter 
in a body, and it has been established that gravity is propor- 
tional to mass. 

If a stone were dropped from a balloon it would fall to- 
ward the earth by reason of the attraction of the earth, or 
terrestrial gravitation. The earth also tends to fall toward 
the stone, but its mass is so much the greater that its motion 
is inconceivably small. 

But gravitation does not always produce motion. A stone 
resting on the top of a table is not free to fall, and, in such 
a case, the force of the earth's attraction is expended in 
pressure against its support. This pressure is called the ab- 
solute weight of the body. Hence, weight is the measure of 
the earth's attraction. 

28. Gravity is also influenced by distance, as will be 
'shown hereafter. An iron ball which weighs one hundred 

and ninety-four pounds at the equator will weigh one hundred 

land ninety-five pounds at the poles. Hence, weight does 

,not always mean the same as mass, for a body will always 

contain the same amount of matter in every conceivable 

place. Nevertheless, as weight is always proportional to 

mass, we may use weight as a means of estimating mass, or, 

| in most instances, use the two terms interchangeably without 

! sensible error. 



20 



ELEMENTS OF PHYSICS. 



29. Universal gravitation is the same force applied to 
the heavenly bodies. It is by reason of this force that the 
earth and other planets move round the sun. 

30. The unit of weight adopted by the United States 
and England is the avoirdupois pound of 7,000 grains. 

The French unit, called a gramme, is the weight of a 
cubic centimetre of distilled water, at 39°. 2 F. A gramme 
equals 15.434 grains; a kilogramme equals 15434 grains, or 
2.2046 avoirdupois pounds. 

Weight in pounds of one cubic foot at 62° F. 



Air, 


0.080728 


Wrought Iron, 480. 


Water, 


62.418 


Copper, 556. 


Mercury, 


848.75 


Lead, 712. 


Potassium, 


53. 


Gold, 1224. 



Gravitation is made serviceable to man in the force of 
running water, and in machinery moved by weights, as well 
as in giving stability to buildings and 
other structures. 

31. The unit of pressure in most 
frequent use is the pressure of one at- 
mosphere. This pressure is due to the 
attraction of gravitation. We may 
ascertain its amount by the experiment 
of Torricelli. 

Fill a glass tube, thirty-two inches 
long, with mercury, close the open end 
firmly with the finger, and then invert 
it in a cistern of mercury, Fig. 4. On 
removing the finger, the mercury will 
fall a little way in the tube and leave 
a vacuum above it. Now, as the FlG - 4 - 

weight of the mercury tends to make it flow out of the 




EXPANSION BY HEAT. 



21 



tube, the column must be sustained by an equal and oppo- 
site force. This force can be nothing else than the pressure 
of the atmosphere; and, hence, this pressure may be meas- 
ured by the mercurial column. This apparatus is called a 
Barometer, and is used to measure the pressure of the air. 
At the level of the sea, and at 32° F., the average height 
of the mercurial column is 29.922 inches, or 760 millimetres. 
A column of this height, a square inch in section, weighs 
14.73 pounds. 

We are accustomed to say that the pressure of the at- 
mosphere is nearly fifteen pounds to every square inch of 
surface. 

Table of Pressures. 



POUNDS ON THE 
SQUARE FOOT. 



POUNDS ON THE 
SQUARE INCH. 



One atmosphere, 2121.12 14.73 

One foot of water, at 39°. 2 F., 62.425 0.4335 

One inch of mercury, at 32° F., 70.73 0.4912 

32. Heat tends to make the molecules of matter re- 
cede from each other. When a body is warmed, it becomes 
larger ; when it is cooled, it contracts. 

The apparatus shown in Fig. 5 illus- 
trates the expansion of solids. This 
consists of a brass ball, so made that, 
at ordinary temperatures, it will pass 
easily through the ring, m. On heat- 
ing the ball, it will no longer pass 
through the ring. 

This increase of volume of a heated 
body must be due to a motion among 
the molecules, which tends continually 
to separate them. When this motion 
increases in intensity, the body be- 
comes warmer; when this motion decreases in intensity, the 




Fig. 5. 



22 ELEMENTS OF PHYSICS. 

body becomes cooler. Hence, we may measure the intensity 
of the heat, or tlie temperature of a body, by the degree of 
the molecular motion, or by the expansion of bodies. 

33. The Thermometer is an instrument which measures 
temperatures. The ordinary mercurial thermometer consists 
of a very small glass tube (Fig. 6), at one end of which 
is blown a bulb — the bulb and part of the tube are 
filled with mercury. When the thermometer is placed . 
near a source of heat, the column of mercury rises, and 
falls when it is removed, because of the expansion and 
contraction of the mercury. The glass also expands 
and contracts, but only one-seventh as much as the 
mercury; and so we have only to notice the apparent 
expansion of the mercury. 

In order to compare temperatures, we assume as • 
standards the temperatures of melting ice and of water 
boiling, under the pressure of one atmosphere. These 
standards are called, respectively, the freezing and the 
boiling points. FlG * 6 - 

For greater convenience, arbitrary scales have been devised 
to designate small variations in the mercurial column. The 
freezing and boiling points are first determined, and the 
height of the column in each case is marked on the tube, or 
on the scale attached to it. The space between these is then 
divided into any number of equal parts, called degrees, and 
parts of the same length set off above and below the boil- 
ing points. 

The Centigrade scale marks the freezing point by 0°, and 
the boiling by 100°. 

Reamner's scale marks the freezing point by 0°, and the 
boiling by 80°. 

Fahrenheit's scale marks the freezing point by 32°, and 
the boiling by 212°. 



MEASUREMENT OF HEAT. 23 

These scales are distinguished by the letters C, R, and F. 
The divisions below zero are indicated by the negative sign. 
Thus, — 10° signifies ten degrees below zero; 10°, or +10°, 
signifies ten degrees above zero. 

To compare these scales, we first notice the interval be- 
tween the freezing and boiling point, and find C = 100°, 
R=80 o , F=180°; hence, these are equal, or 1°C = 
4° R = |° F. Now, if we remember that the zero of 
Fahrenheit's scale is 32° below the freezing point, we may 
convert one scale into another, thus : 



°F = f °C + 32° 


°F = | °K-f-32° 


°C= (°F — 32°) f 


°R= (°F — 32°) f 


°C = | °R 


°R=i°C 



34. The amount of heat in a body must not be con- 
founded with its temperature. It is evident that a pint of 
boiling water would have the same temperature as a gallon 
of boiling water, and would equally affect a thermometer. 
The relative amount of heat present in a body is measured by 
the thermal unit. This is the quantity of heat required to 
raise a pound of water from 32° F. to 33° F. Hence, a 
gallon of boiling water would contain eight times as many 
thermal units as a pint, and would be competent to melt 
eight times as much ice or snow. 

35. The force of light is closely related to that of heat. 
It may seem strange that it is reckoned as a force ; but it is 
easy to show that it may produce change in matter. Thus, 
if the gases hydrogen and chlorine are mixed in equal quan- 
tities in the dark, they will not combine ; but if exposed to 
the free sunlight, they will unite with explosive violence. 
The photographer's art depends on the force of light. Soak 
a strip of white newspaper in common salt brine and let it 
dry ; when dry, again moisten it in a darkened room with a 



24 



ELEMENTS OF PHYSICS. 



sponge dipped in a solution of silver nitrate, and again dry 
it. This process covers the paper with white silver chloride. 
Now if this coated paper be placed in the sunlight, it will 
darken, showing that the light effects a change in the silver 
chloride. Moreover, in the grand laboratory of nature, light 
is an essential force. To define it, we select one of its prop 
erties and say that " light is that mode of motion which ex- 
cites in us the sensation of vision." 

36. The force of electricity is familiar to all, in its ap- 
plications to the telegraph, in the magnet, and in the flash 
of lightning. 

Its simplest effects may be shown by rubbing a glass rod 
briskly upon the coat-sleeve, and then presenting the rubbed 
end to small and dry pieces of paper. If the air is not too 
damp, the paper will be attracted to the rod, cling to it for a 
little while, and then fly off. 
Instead of the bits of paper, 
we may employ a light pith 
ball, suspended by a silk 
thread, Fig. 7. The ball will 
be first attracted and then 
repelled by the excited rod. 
We may use this phenomenon 
to define electricity as a force 
which becomes manifest by 
its peculiar phenomena of 
attraction and repulsion. fig. t. 

37. These are the only forces of inanimate nature of 
which we have any certain knowledge. 

They produce, by their action upon matter, secondary 
forces, which are employed by man in machines. Thus, the 
strength and elasticity of springs is mainly due to cohesion ; 
the action of glues and cements, to adhesion; the elastic 




CONSERVATION OF FORCE. 25 

force of steam, to heat; the power of running water, or of 
falling weights, to gravitation ; the muscular strength of 
men, to cohesion, affinity, etc., modified by the vital forces. 

38. However forces act upon bodies, the matter of 
which they are composed is not lost. When gunpowder is 
exploded, it disappears, leaving only for a moment a trace of 
smoke. It has, however, only undergone a chemical change, 
by which a part of its ingredients have been converted into 
gases. If the explosion is made in a sealed vessel, suffi- 
ciently strong to stand the shock, the vessel and its contents 
will not change in weight by the operation. Matter is in- 
destructible by any force that man can employ upon it. 

We are also justified in asserting that force is indestruct- 
ible. Affinity, electricity, heat, and light, are so closely 
allied that the action of any one may induce the action of 
any other : thus a candle burns by reason of affinity, and 
gives out heat and light. For this reason these four are 
called correlative forces. 

Natural Philosophy or Physics treats of the physical 
changes which are produced by the action of force upon 
matter. 

Recapitulation. 

Bodies are classified 

C Solid, as ice. 
I. With regard to state as ■< Liquid, as water. 

V Aeriform, as steam. 

tt ttt-^ i *. f Simple, as oxygen. 

II. With regard to composition, i 

( Compound, as water. 

Forces act 

I. Only on molecules, II. Also, on bodies, 

! Cohesion. 
Adhesion. 
Affinity. 



Electricity. 
Light. 
Heat. 
Gravitation. 



Phys. 3. 



1 v i^y\ i-\j? 

* 26 ELEMENTS OF PHYSICS. 



? 



The general properties of matter are — magnitude, weight, impene- 
trability, mobility, inertia, divisibility, porosity, compressibility, ex- 
pansibility. 

We estimate the action of forces by certain units. Among these 
are units of measure, units of volume, units of time, units of weight, 
units of pressure, units of heat. 

Problems. 

1. How many centimetres are there in 29.922 inches? 

2. How many inches are there in 0.994 metres ? 

3. How many square inches are there in a circle of one inch radius? 
of two inches radius? What is the ratio between the two areas? 
How many square centimetres are there in each circle ? 

4. How many cubic inches are there in one pint? How many 
cubic centimetres? How many litres? 

5. How many litres are there in a sphere of six inches radius? of 
one foot radius? What is the ratio between the two volumes? How 
many gallons are there in each sphere ? 

8. What will be the weight of each sphere if made of air? of 
water? of gold? Reckon each in pounds and also in grammes. 

7. What will be the edge of a cube containing ten pounds of 
water? the radius of a sphere containing an equal weight of water? 

8. From the table of specific gravities calculate the weight of a 
gallon of oxygen, of sulphuric acid, of cork, of silver. 

9. What does a litre of dry air weigh in grammes? 

10. What is the average velocity per minute of a locomotive that 
passes over 138 miles in six hours? 

11. What will be the atmospheric pressure on a surface of six 
square inches in pounds? in grammes? On a surface of six inches 
square, in pounds? in kilogrammes? 

12. What is the atmospheric pressure on one square centimetre in 
kilogrammes? 7 j ' fV^ m 

13. Convert 25° C. to °F.; 50° C. to °F. Can you say that 50° C. 
is twice as hot as 25° C. ? f j 

14. Convert 62° F. to °C. ; 39°.2 F. to °C. If 

15. If a gallon of boiling water will melt ten pounds of ice, how 
much will be required to melt one cubic foot ? 



Xdr 












CHAPTER II. 

PHENOMENA CONNECTED WITH COHESION. 

39. The cohesion of solids may be estimated by the 
resistance which they offer to forces which tend to separate 
their particles. 

There are many ways by which the strength of a body 
may be tried. Among these are : 

(1) By a stretching force. — We may hang a rubber tube 
from a hook, and pull it downward by a weight. The rubber 
will stretch, and, with a weight sufficiently heavy, will be 
torn in pieces. The resistance which a body offers to a 
stretching force is called its tenacity. The tenacity of metals 
is increased by drawing them into wires. A cable made 
of wires twisted together is far stronger than a chain of 
equal weight. Wire cables are used in suspension bridges 
for this reason. The suspension bridge at Cincinnati has 
a span of one thousand feet. 

(2) By a compressing force. — If we place a weight on a 
small bar of wood, it will compress its particles and tend to 
crush the bar. When the bar is not allowed to bend, it 
offers the same resistance to pressure that it would to a 
stretching force. 

(3) By a bending force. — If we fasten one end of a lath, 
placed horizontally in a vice, and apply a weight at the other 
end, it will bend and tend to break. The strength which the 
substance exhibits depends not only on the material but also 
on the manner in which the strain is applied. A sudden 
shock causes a much greater strain than a gradually increas- 
ing force of greater amount. So, also, the lath will support 

(27) 



28 



ELEMENTS OF PHYSICS. 



a greater weight when its broad side is placed vertically than 
when it is horizontal; then, also, the longer it is the less 
weight it will support. Finally, if both ends are supported, 
it will sustain half the weight, when it is concentrated at the 
center, that it will when distributed along its whole length. 
What is true of the lath, is also true of the beams used in 
houses, they are placed so as to receive the strain on their 
edges. 

The bones of animals, and the stalks of grain, are hollow. 
This is the most economical arrangement of a given weight 
of material. We may illustrate 
this fact by resting the ends of 
a flat sheet of paper on bricks, 
and ascertaining the force neces- 
sary to break it down ; then re- 
peat the test with a similar sheet 
of paper after having coiled it 
into a tube, Fig. 8. If a broad 
strap is used to hang the weight from, a closely coiled tube 
of this sort will support three or four times as much weight 
as before. 

(4) By a twisting strain. — Suppose, when the lath is in the 
vice, we attempt to twist it. The force will tend to wrench 
the particles asunder; and it is possible that we may ac- 
complish this with a long and thin lath. The kind of 
strength that resists a twisting strain is called resistance 
to torsion. 

40. The effective strength of any structure is that which 
is not employed in supporting the weight of the structure itself. 
It would be impossible to build such roofs and bridges of 
iron as have been built of wood, because the strength of the 
material would not be sufficient to support its own weight. 
Pine, which has nearly half the tenacity, has only one-tenth 




Fig. 8. 



ANNEALING. 29 

the weight of iron ; so that, for equal weights, pine has 
more than four times the tenacity of cast-iron. Steel has 
the greatest tenacity known. A rod of steel, one foot long 
and a square inch in area, w r ill support a weight of 130,000 
pounds. 

41. If a body does not give way on the application of 
a strain, it is frequently permanently changed in shape. A 
stretching force may draw some bodies into a wire-shape. 
Such bodies are ductile. Glass is very ductile when at a red 
heat, and may be drawn into very delicate threads. A com- 
pressing force flattens some bodies into thin sheets. Such 
bodies are malleable. Most metals are both malleable and 
ductile, though not in equal degrees. Gold is the most 
malleable, and platinum the most ductile of metals. 

42. A sudden blow often breaks many bodies that in 
other respects are quite strong. Such bodies are brittle. 
Glass is a good example. A bottle that will resist a great 
pressure is broken by a gentle blow from some hard sub- 
stance. A hard substance is frequently also brittle. We 
measure the hardness of a body by the readiness with 
which it is scratched by another substance. The diamond 
is the hardest body known. Quartz is hard enough to 
scratch glass. 

43. When steel is strongly heated, and then suddenly 
cooled, it becomes very hard, and so brittle that it is suit- 
able only for the dies used in coining, and for the hardest 
files. On the other hand, if it is cooled slowly, it becomes 
softer, more ductile, and tenacious. This process of slow 
cooling is called annealing. Steel is tempered by first harden- 
ing it, and then a portion of its hardness is removed by 
reheating the steel to a lower temperature than at first, and 
then cooling it gradually. The temper required depends on 
the use to which the steel is to be applied. Surgical instru- 




30 ELEMENTS OF PHYSICS. 

ments require a hard, keen edge ; table knives require more 
flexibility ; and springs require both flexibility and tenacity. 
The effect of rapid or slow cooling in glass is about the 
same as in steel. Melted glass dropped into water solidifies 
into the curious toy known as Prince Rupert's drops, Fig. 9. 
The body of these drops is so hard that it will bear 
a smart blow ; but if the tail be broken, the whole 
flies into minute particles. This brittleness is pre- 
vented in glass utensils by carefully annealing. As 
soon as the glass vessels are blown, they are drawn 
through a long furnace in which the heat gradually FlG * 9 * 
diminishes from one end to the other. The thicker the 
glass, the longer the time required in annealing. 

44. The phenomena just considered involve a perma- 
nent displacement of the particles of a body. If the strain 
does not exceed a certain limit, the body will resume its 
previous shape, when the force has ceased to act. The en- 
ergy with which the particles resume their original position 
is due to their elasticity. Up to the limit of elasticity, the 
elastic force is exactly equal to the strain, and the elasticity 
is therefore perfect. Beyond this limit, brittle bodies break : 
the molecules of most other solids are permanently displaced, 
or set, w r ith new relations to elasticity, exactly similar to the 
first. Thus : when a wire has been permanently lengthened 
by a great strain, it is still enabled to manifest perfect elas- 
ticity by recovering from a smaller strain. 

Flexibility should not be confounded with elasticity. A 
wire of soft iron is very flexible, though but slightly elastic ; 
that is, it may be readily bent, but does not recover its posi- 
tion when the force is removed. A steel spring is both flex- 
ible and elastic. 

45. The elasticity developed by compression belongs to 
all bodies, whether solids, liquids, or gases. All fluids are per- 



ELASTICITY. 31 

fectly elastic. Liquids are but slightly reduced in volume under 
ordinary pressures. Gases decrease in volume as the pressure 
exerted upon them iucreases; if the pressure be doubled, the 
volume will be one-half, etc. When the pressure is removed, 
both liquids and gases resume their original volume. 

The elasticity of aeriform bodies is exemplified by a boy's 
pop-gun. The air between the wad and the piston increases 
in elastic force as it decreases in volume, until the elasticity 
is sufficient to expel the wad. 

The elasticity of such solids as India rubber, ivory, and 
steel, is very great. If a ball of ivory or of glass be dropped 
on a slab of marble, it will rebound to a height nearly equal 
to that from which it fell. If the slab had been covered 
with oil, it would be found that the ball had left a circular 
impression on the plate, and had itself received a blot of 
oil. On repeating this experiment, it will be seen that the 
size of the spot on the slab and on the ball increases with 
the height from which it falls. It appears, therefore, (1) 
that the ball was compressed at the moment of the shock ; 
(2) that the rebound was caused by the effort to regain its 
shape ; (3) that the elastic force increases with the strain. 

Lead, clay, and the fats receive a set with only a moderate 
compressing force, and, therefore, have but little elasticity. 

46. The elasticity of musical strings is developed by 
stretching. The tendency that twisted strings have to un- 
twist exemplifies the elasticity developed by torsion. The 
elasticity, developed by bending, is splendidly shown in glass 
threads : in them it is perfect, as they never receive a set, 
but break when the limit of elasticity is passed. 

47. The practical applications of elasticity are innu- 
merable. The elasticity of solids is applied in the springs 
used in watches, clocks, carriages, bows, spring-balances, etc. 



32 ELEMENTS OF PHYSICS. 

The elasticity of air is turned to account in foot-balls, air- 
cushions, air-springs, etc. 

Kecapitulation. 

The properties which have been considered in this chapter are 
called the specific properties of bodies. They fall into two classes : 

Tenacity, 

Resistance to pressure, 
I. Those involving strain of particles, ^ Resistance to bentf.ing, 

Resistance to torsion, 
Elasticity. 
Ductility, 

II. Those involving permanent displace- J Malleability, 
ment of particles, J Hardness, 

Brittleness. 



r 



CHAPTER III. 

PHENOMENA CONNECTED WITH ADHESION. 

48. The force of adhesion gives value to cements : thus 
glue is used for wood ; gum mastic and shellac for glass ; dex- 
trine for paper ; etc. This choice of cements for different 
objects shows that adhesion varies with the kind of matter. 

Some of the phenomena of adhesion have received specific 
names, and are of great importance. Among these are the 
following : 

49. Capillary action. — If a clean glass plate is dipped 
vertically in water, the liquid will rise on each side to the 
height of nearly one-sixth of an inch, 
Fig. 10. It must be evident that the 
weight of this liquid column is sup- 
ported by the adhesion of the water 
to the glass. A second plate will sup- 
port an equal weight; and, hence, if 
two parallel plates are brought so near 
each other that both may act on the 
same molecules of the liquid, the 
column of the water will rise higher. 
The nearer the plates, the higher will 
the liquid rise, Fig. 11. Two plates, one- 
hundredth of an inch apart, will sup- 
port a column of water two inches high. 

When two plates are inclined to- 
ward each other, as in Fig. 12, the 
water takes the shape of the curve known as the equilateral 
hyperbola. 

(33) 




Fig. 10. 




Fig. 11. 



34 



ELEMENTS OF PHYSICS. 




Fig. 12. 



Finally, if a tube is substituted 
for the plates, the molecules of 
the liquid will be attracted on all 
sides, and the water will rise to 
twice the height produced by 
two plates, separated by a space 
equal to the diameter of the tube. 
If the tube has a diameter of one- 
hundredth of an inch, the column 
of water will be four inches high. 

50. The adhesion which causes liquids to rise on solids 
is called capillary attraction, because it is best exhibited in 
very small hair-like tubes. 

Liquids do not rise in tubes unless they wet them ; if they 
do not wet them, they are depressed. A needle, slightly 
greased, can be made to float on water, because, not. being 
wet by the liquid, it produces a depression in which it is 
supported. For the same reason mercury is depressed by a 
glass plate, but rises freely on lead and some other metals. 
The amount of ascent and depression varies with the sub- 
stances used: thus, in a glass tube, alcohol will rise about 
one-half as much as water — mercury is depressed in a glass 
tube, and its surface is convex, while water exhibits a con- 
cave surface. 

51. Familiar illustrations of capillary attraction are 

seen in the action of lamp-wicks. Blotting paper readily 
draws ink into its pores, which resemble short capillary 
tubes. The pores in writing paper are closed by sizing. If 
one end of a towel is dipped in a basin of water, and the 
other left hanging over the edge, the whole towel will be- 
come wet. Water can not be poured out of a full tumbler 
without running down the outside because of the adhesion 
of the water to the glass. 



SOLUTION. 35 

In the droughts of summer the water necessary to the 
support of vegetation is drawn toward the surface of the 
ground by capillary action. It is also one of the principal 
causes of the ascent of sap in plants, and plays an essential 
part in the circulation of liquids in animal tissues. 

52. Solution. — If a lump of sugar is dipped in water, 
the liquid will rise by capillary attraction until the whole 
is moistened. If enough water is present, the sugar will 
entirely disappear in the liquid, thus forming a solution. 
This shows that the adhesive force is sometimes sufficient to 
overcome the cohesion of solids. Each drop of the solution 
is sweet like sugar, and fluid like w r ater, showing that the 
adhesion is perfect, because it is shared by every molecule. 
A solution is said to be saturated when no more of the solid 
will dissolve in it. 

53. The solvent powers of liquids vary exceedingly. 
An ounce of cold water will dissolve two ounces of sugar, 
although it can dissolve hardly a grain of sulphate of lime. 
Fats dissolve in ether, benzine, and bisulphide of carbon ; 
resins dissolve in alcohol ; lead and gold in mercury. 

When a metal disappears in an acid, as copper in nitric 
acid, the action has two stages: (1) a chemical action by 
which the solid and liquid unite to form a substance differ- 
ent from either, as nitrate of copper; (2) a simple solution 
by which the compound thus formed dissolves in the liquid. 

54. Gases also dissolve in liquids. — The rapidity with 
which w T ater absorbs ammonia may be prettily shown by the 
following experiment: halving fitted a glass tube, tapering at 
one end, to the cork of a large bottle, fill the bottle with 
dry ammonia gas. Then invert the bottle in water, Fig. 13. 
After a little time the water will absorb so much of the gas 
as to leave a partial vacuum in the bottle; the pressure of 



36 



ELEMENTS OF PHYSICS. 




Fig. 13. 



the atmosphere will then force the water up 
the tube and form a small fountain. 

One volume of water absorbs 1049 volumes 
of ammonia, 506 volumes of hydrochloric acid, 
and nearly twice its volume of carbonic acid. 

55. The weight of any gas absorbed by 
a liquid varies with the pressure; that is, if 
the pressure be doubled or tripled, the weight 
of the gas absorbed will be doubled or tripled. 
The effect of pressure on a gas is to diminish 
its volume and increase its weight in propor- 
tion to the pressure. Therefore the volume of the gas 
absorbed is the same for all pressures. If the pressure is 
removed, the gas resumes its original density, and escapes 
with effervescence. The "soda water" of the confectioner 
is water charged with carbonic acid gas, absorbed . under 
pressure. 

56. Porous solids like charcoal, dry clay, and metals in 
a state of fine division, often absorb large amounts of gases. 
One volume of charcoal will absorb 35 volumes of carbonic 
acid, and 90 of ammonia. A piece of freshly burned char- 
coal, exposed to the air for a few days, will often increase 
one-fifth in weight. This phenomenon can be explained by 
the supposition that the solid, by reason of its porous condi- 
tion, offers a very large extent of surface, to which the gases 
adhere, and bectfme condensed. Finely divided platinum 
absorbs 250 times its volume of oxygen. 

57. The absorptive power of charcoal is of great eco- 
nomic value. The variety known as bone-black is used for 
clarifying sugar. The brown sirups are filtered through a 
layer of bone-black twelve or fourteen feet in thickness, and 
are thus obtained perfectly clear, all the coloring matters, 
whether solid or liquid, being perfectly absorbed. Ale and 



DIFFUSION. 37 

porter filtered through animal charcoal lose much of their 
bitterness, and all of their gases. All varieties of charcoal 
are efficacious in absorbing the gaseous products of decaying 
animal matters, and, thereby removing noxious effluvia from 
the air. 

58. Solids also adhere to gases. — The transportation 
of dust by the winds is a proof of this. This action, if 
continued for a long series of years; may effect great physical 
changes, as is seen in the shifting sands of the deserts, and 
in the sandy hills, called dunes, that are formed on the 
coasts of France. 

59. When fluids mix with each other without entering 
into chemical union, it is because of the mutual adhesion of 
their molecules. Some liquids, like water and alcohol, or 
glycerine, are miscible in all proportions. If equal volumes 
of water and ether are shaken together, and then allowed 
to stand, they will, in great measure, separate, each liquid 
dissolving about one-tenth of the other. The adhesion of oil 
and water is so feeble that they can not be made to mix per- 
manently by any amount of shaking and stirring. 

Any two gases will form a permanent mixture 
when they are placed in the same vessel, if they 
do not enter into chemical combination. 

60. The tendency of fluids to mix with 
each other is called diffusion. Diffusion may 
take place without stirring or shaking, and 
even in apparent opposition to the attraction 
of gravitation. Thus, if a tall jar is partially 
filled with a solution of blue litmus, or water in 
which a red cabbage has been boiled, and sul- Fig. h. 
phuric acid is carefully poured througli a long funnel (Fig. 
14), reaching to the bottom of the jar, the line of separation 
between the two liquids will be, at first, distinctly marked. 




38 



ELEMENTS OF PHYSICS. 




Soon the acid will rise and the water will sink, until the two 
are perfectly mixed. This will, however, require some time, 
and the progress of diffusion may be traced from hour to 
hour by watching the gradual change from blue to red. 
This may be repeated with any two miscible fluids, as cab- 
bage water and a solution of caustic soda. 

61. The diffusion of gases may be illustrated by the 
apparatus shown in Fig. 15, which con- 
sists of two bottles, connected by a 
lohg glass tube. 

Fill the upper with the lighter gas, 
as hydrogen, and the lower with a 
heavier, as chlorine. The greenish color 
of the chlorine enables us to trace 
its gradual ascent. In a few hours the 
two gases will mix perfectly and perma- 
nently. This experiment should be 
performed only in a darkened room so 
as to avoid an explosion. 

The diffusion of gases is of the greatest 
importance in maintaining the purity of 
the atmosphere. The constituents of the 
air are of different specific gravities, m^ ^ 
and would arrange themselves with the Fig. 15. 

heaviest at the bottom if it were not for this beneficent law 
of nature. The carbonic acid, a product of decay and com- 
bustion, would be found at the surface of the earth, and 
destroy all animal life. As it is, the noxious gases are 
rapidly diluted when formed, and soon are so perfectly dis- 
seminated through the air, that chemical analysis fails to 
find any essential difference in the air of mountain, plain, 
or valley. 

62. Osmose is a term used to denote the diffusion of 




OSMOSE. 



39 



fluids when they are separated by a porous partition or 
septum. The presence of the septum greatly modifies the 
phenomena of diffusion. 

Tie a glass tube to the mouth 
of a bladder, Fig. 16, fill the 
bladder with strong brine, su- 
gar sirup, or alcohol, and then 
immerse it in pure water. After 
a while it will be found that the 
liquid has risen in the tube, and 
that the outer vessel contains 
some of the substance that was 
in the interior. Hence, a cur- 
rent has been produced in two 
directions. The one passing in- 
to the bladder is called endos- 
mose; the one passing out, exos- 
mose. The rate of diffusion 
is greater in osmose than in 
simple diffusion. 

Instead of the bladder, an inverted funnel, having its 
mouth closed by a strip of any animal membrane, or by 
parchment paper, may be used. 

63. Dialysis is the application of osmose to the separa- 
tion of mixed solutions. If a solution contains alcohol, 
hydrochloric acid, or crystallizable bodies like sugar, they 
will pass through the septum ; but gum-arabic, gelatine, 
and other substances that do not crystallize, will not, 

64. The osmose of gases may be shown by a striking 
experiment. 

Close the mouth of a long glass funnel with a septum of 
plaster of Paris. This may be done by making a moderately 
thick paste of the plaster with water on a plate, inverting 




Fig. 16. 



40 



ELEMENTS OF PHYSICS. 



the mouth of the funnel therein, and then suffering the 
plaster to harden. After drying the septum, place the tube 
in colored water, and invert over the closed mouth a jar 
filled with hydrogen, Fig. 17. The 
endosmose of the hydrogen will soon 
become manifest by the escape of bub- 
bles through the water. Remove the 
jar, and the hydrogen will escape from 
the funnel in a contrary direction, as 
may be seen by the rise of the water 
in the funnel tube. 

Although the nature of osmose has 
not been satisfactorily determined, it 
is manifest from the porous nature 
of animal and vegetable membranes, 
that it must play an important part in 
the operations of life. In breathing, 
the lungs give out carbonic acid by 
exosmose, and absorb oxygen by en- 
dosmose. It is probable that the ascent 
of sap in plants, and the various pro- FlG - 17 - 

cesses of secretion in animals are either controlled or essen- 
tially modified by osmotic action. 




Recapitulation. 



The force of adhesion is shown in 
I. Cements and Friction 
II. Capillary action 

III. Solution of solids 

IV. Solution of gases 
V. Absorption of gases 

VI. Shifting sands - 
VII. Diffusion of liquids 
VIII. Diffusion of gases 
„IX. Osmose - 



Solids to solids. 
Liquids to solids. 
Solids to liquids. 
Gases to liquids. 
Gases to solids. 
Solids to gases. 
Liquids to liquids. 
Gases to gases. 
Diffusion through septa. 



CHAPTER IV. 

THE LAWS OF MOTION. 

65. A body at rest remains at rest; a body in motion 
will continue moving with uniform velocity in a straight 
line, unless it is acted upon by some external force. This 
statement is known as the law of inertia, or as the first law 
of motion. 

It is difficult to furnish examples which will perfectly 
illustrate this law. Our experience teaches us that a body 
will not move unless some force acts upon it; but that a 
moving body will continue in motion, is not so self-evident. 
Now let us roll a ball along the ground, then on a smooth 
floor, then on the ice : the fewer the obstacles in the way, the 
more direct will be its course, the longer will it continue in 
motion, and the more uniform will be its velocity. So, also, 
if we spin a heavy top in the air, and then in a vacuum, it 
will continue moving much longer in the latter case than in 
the former. All moving bodies on the earth's surface meet 
with opposing forces, such as gravity, friction, and the resist- 
ance of the air. The examples given above show that the 
more we can reduce these opposing forces, the nearer will the 
motion correspond to the law. If we could conceive of a 
body set in motion by a single impulse, and then left to 
itself, its motion would be in exact conformity to the law. 

66. To comprehend the action of a force, three things 
must be known. (1) The energy with which it acts in a 
unit of time: this may be expressed by the pressure it 
exerts, or by its power of doing work, and may be repre- 
sented by a straight line. (2) The direction, or the line along 

Phys. 4. (41) 



42 ELEMENTS OF PHYSICS. 

which it acts; and (3) the point of application, or the point 
upon which it exerts its action. In stating the theoretical 
action of forces, such external forces as friction, and the 
resistance of the air, are generally left out of account. 
This fact must be borne in mind when experiments are 
made intended to illustrate the action of forces. 

67. A force which acts for an instant and then ceases 
to act is called an impulsive force. Projectiles, like bullets 
and arrow r s, are set in motion by impulsive forces. A con- 
stant force acts with the same energy without, ceasing. It is 
convenient for us to consider a constant force as due to an in- 
finite number of equal successive impulses, each one of w r hich 
acts through a very brief interval of time. Gravity is a con- 
stant force. A locomotive under head of steam that is kept 
constant is another. A constant force tends to produce a 
velocity that increases at each successive instant. Thus, a 
locomotive starts slowly, and rapidly increases its rate of 
motion ; but after awhile it moves with uniform velocity, 
because the friction and the resistance of the air also 
increase so that they are exactly equal to the motive pow T er 
of the engine. 

68. Simple motion is produced by the action of a single 
force. Compound motion is produced by the joint action of 
two or more forces. A ball falling in a perfect vacuum is 
an example of simple motion. A ball falling in the open 
air is an example of compound motion. 

It is well to consider some other examples of compound 
motion. Suppose a boat, impelled by oars on quiet water at 
the rate of four miles an hour, enters a river whose current 
is three miles an hour, then, (1) if the boat go down the 
river, its speed will be seven miles an hour ; (2) if the boat 
go up the river, its speed will be one mile an hour; (3) if 
the boat is rowed directly across the river, its speed will be 






COMPOUND MOTION. 43 



five miles an hour. Let AB be the direction of the boat, 
and AC the direction of the current ; that is, let these two 
lines represent the motion that would be 
produced if only one force were acting at a 
time. If both are acting at the same time, 
the actual direction of the boat will be the 
line AD, which is the diagonal of the paral- ^ 
lelogram ABCD. This line also represents 




B 

X 



the intensity of the joint action of the two FlG - 18 - 

forces; and the boat will move as if impelled only by a 
single force in the direction of the line AD. 

A single force that represents the effect of two forces 
taken together is called their resultant. When the forces, as 
in the third case, are at right angles to each other, the find- 
ing of their resultant is the problem of finding the hypotenuse 
when two sides of a right-angled triangle are given. 

Thus, 3 2 + 4 2 =5 2 . 

69. Illustrations of compound motion. — When a 
steamboat is in motion, all the objects on it partake of 
the onward motion of the boat. Balls may be thrown and 
caught with the same certainty as on shore. But the direc- 
tions which these balls take when referred to the ground 
beneath the boat will be the resultants of the motion of the 
boat, and the motions which the players give to the balls. 
So, also, an acrobat as easily goes through his feats of skill 
on the back of a horse in rapid motion as he would on the 
ground. 

Conversely, when we have the resultant of two or more 
forces, we may find its components. As an illustration, take 
the sailing of a sloop under a wind oblique to the course of 
the boat. Represent the direction of the wind by the line 
Vm. Its force may be resolved into two components: the 
one, ttf, tangent to the sail, and producing no effect; the 



44 



ELEMENTS OF PHYSICS. 



other, mn, perpendicular to the sail. As the sail is oblique 
to the axis of the boat, this force will tend to give the boat 
a lateral motion, called the leeway. Therefore, this force is 
again decomposed by the keel and the rudder, and the re- 
sultant impels the boat on its course. 

These are examples of the second law of motion, which 
is : If two or more forces act together on a body, each force pro- 
duces the same effect as if it were acting alone. 




Fig. 19. 

70. The measure of force. — We can now understand 
that if a given force, acting for one second upon a mass, will 
generate a certain velocity ; a double force, acting for one 
second, will generate twice the velocity. So, also, if it re- 
quires a given force to impart a certain velocity to a mass, 
it will require double the force to produce the same velocity 
in twice the mass ; for if the double mass were halved, and 
half the force applied to each, placed side by side, the ve- 
locity would be the same. Hence, the product of the mass 
by the velocity is one measure of force. This product is 
called momentum. 



CIRCULAR MOTION. 45 

Thus, the momentum of a body weighing five pounds, and 
moving with a velocity of four feet per second, is twenty. 
That is, it would require twenty units of force, acting in the 
opposite direction for one second, to produce pressure enough 
to bring the body to rest. The momenta of large bodies, 
moving very slowly, are sometimes enormous. The momenta 
of icebergs are irresistible by any human power, even though 
their motion be so slow as to be almost imperceptible. 

There is also another measure of force, which is termed 
energy, or the power of doing work, which we shall consider 
hereafter. 

71. The unit of work is the force required to raise one 
pound one foot high. This is called the foot-pound. The 
unit of poicer is the force required to raise one foot-pound in 
one second of time. A horse-power is the mechanical value 
of a force capable of raising five hundred and fifty pounds 
one foot high in one second. Its work is, therefore, five 
hundred and fifty foot-pounds in one second. 

72. Circular motion. — It follows from the first law of 
motion that a single force will produce 
motion in a straight line. It follows from 
the second law that if a moving body 
deviates from its original direction, a 
second force must be acting upon it. If a 
body moves in a circle, w T hich is a con- 
stant series of deviations from a straight figT^cT 
line, it must be acted upon by a constant force, in addition 
tp the impulse which urges it in a straight line. 

If a ball be whirled in a circle by means of a rubber cord 
held by the hand, we feel the cord stretched by a sensible 
force pulling outward — the hand resists this by pulling in- 
ward. If the cord is cut, the outward force will carry the 
ball in the direction of the tangent to the circle, as AT; 




46 



ELEMENTS OF PHYSICS. 



but when the two forces are equal, the curve is that of a 
circle. Circular motion is produced by the action of two 
forces, one of which, at least, is a constant force. The force 
that tends to draw bodies to the center, is called the centri- 
petal force; that which tends to drive bodies from the center, 
is called the centrifugal force. 

73. The tendency of revolving bodies to fly off at a 
tangent is easily illustrated. A stone let go from 
a sling, the mud flying off from the wheels of 
a carriage in rapid motion, are examples. If 
a glass globe, containing a little colored water 
and some mercury, is swiftly revolved by a 
twisted string, both fluids will be whirled away 
from the axis; the mercury, having the greater 
relative weight, w T ill occupy the equator, with a 
belt of water on each side, Fig. 21. In laundries 
clothes are dried by placing them in a wire basket 
which is then revolved many hundred times in a 
minute. The centrifugal force may be made to counteract 
gravity: thus, if a cup of water be balanced on the inner 
face of a hoop, by beginning 
with a series of short swings, 
the cup and its contents may 
be whirled over the head with- 
out spilling the water. 

74. Newton proved that 
the shape of the earth is pre- 
cisely that which a globe of 
plastic material would take by 
virtue of centrifugal force. The 
cause of the flattening of the 
earth at the poles may be illustrated by passing an axis 
through two thin hoops of tin, and then twirling them 




Fig. 21. 




Fig. 22. 



ACTION AND REACTION. 



47 



round with moderate velocity; they will take the shape shown 
in Fig. 22. Of course, the upper part of the hoop must be 
free to slide up and down on the axis. 

75. The third law of motion asserts that action and re- 
action are always equal, and are in opposite directions. When 
a weight rests upon a table, the table resists the pressure 
with an equal force. When a ball is fired from a cannon, 
the cannon recoils with a momentum equal to that of the 
ball, but its backward velocity is much less because of its 
greater weight. A bird, in flying, beats the air with its 
wings, and by giving a stroke whose reaction is greater than 
the weight of its body, rises with the difference. If we could 
imagine the bird beating its wings in a vacuum, there could 
be no reaction, and . the 
bird could not move. So, 
in walking, we are assisted 
by the reaction of the 
ground to the pressure \v r e 
exert. 

76. The reaction of 
solids may be showm by 
balls hung from a frame 
so that their diameters 
shall lie in the same 
horizontal line. 

Suspend two equal ivory 
balls from the frame, in 
Fig. 23, and let b fall from 
D upon U. If both balls 
were perfectly elastic, b will 
lose half its velocity in com- Fig. 23. 

pressing V , and the body V will destroy an equal amount in 
regaining its shape ; therefore, b will lose all its velocity and 




48 ELEMENTS OF PHYSICS. 

remain at rest. The other ball, U , will acquire all the ve- 
locity of b, and move to C, a distance, on the other side, 
equal to D. 

If the experiment is repeated with non-elastic balls of 
clay, both will move forward : the momentum of the falling 
body will be communicated to the one at rest, and the united 
momenta will be equal to that of the falling ball. They will 
therefore rise to a less distance than C. 

77. When bodies strike a fixed plane they rebound 
by reason of the reaction of the plane. Suppose a perfectly 
elastic ball falls from P, Fig. 24, 
upon a perfectly elastic plane, 
AB. It will rebound to the 
height from which it fell. Now 
suppose it thrown in the direc- 
tion of IN, the force of the col- ' 
lision at N will be resolved into 
two components : the one, NE, j) 

parallel to the plane AB, which Fig. 24. 

represents its velocity, in the direction of the plane; the 
other component, ND, perpendicular to AB, represents 
the elastic force tending to urge the ball in the line NG. 
By reason of these two components the ball will take the 
direction NR, which is the diagonal of the parallelogram 
NERG. 

The angle INP is called the angle of incidence; the angle 
PNR is called the angle of reflection. In the reflection of 
perfectly elastic bodies, the angle of incidence is always equal 
to the angle of reflection. When either body is not perfectly 
elastic, the component NG will be proportionally smaller; 
hence, the body will proceed, after reflection, in a line nearer 
the plane than NR, and the angle of reflection will be greater 
than the angle of incidence. These facts may be illustrated 






REACTION IN SOFT BODIES. 49 



by bounding balls of rubber, ivory, clay, putty, etc., upon a 
hard floor. 

78. The reaction in soft bodies is not instantaneous, 
and the destructive effect is less. Thus, if a man leaps from 
a height into deep water, the reaction is the same as though 
he alighted on a solid plane, but it is diffused through a 
sufficient interval of time to render it comparatively harm- 
less. Even soft bodies require some time for the displace- 
ment of their particles. If the surface of water be struck 
sharply with the open palm, the blow is met by considerable 
resistance. The sport of "skipping stones" on water ex- 
emplifies this power of resistance for the moment. 

Recapitulation. 

There are three laws of motion. The first declares that the appli- 
cation of force is necessary to move a body from a state of rest; the 
second, that if two forces act upon a body at the same time, each 
acts as if it were acting alone ; the third, that the application of a 
force requires the agency of some external body. 

Problems. 

1. Find the resultant of two forces that may be represented by 7 
and 11 : . C~ .^ 

(a) When they act in the same direction. / *y 

(b) When they act in opposite directions. H r - : . 

(c) When they act at right angles to each other. / y* // 

2. Find the momentum of a body whose weight is 5 tons, and *J l* 
whose velocity is 5 feet per minute. With what velocity must a 
second body, whose weight is 5 pounds, move in order that it may 

have a momentum equal to that of the first body? 

3. How many units of work are required to raise 10 cubic feet of 
water 34 feet high? 

4. How many horse-powers are required to raise 6 cubic feet of 
water each minute to the height of 100 feet? ^~* 

7 



Phys. 



CHAPTER V. 




Fig. 25. 



PHENOMENA CONNECTED WITH GRAVITATION. 

79. Weight has been defined as a measure of the earth's 
attraction. If a lead ball be suspended by a string, it con- 
stitutes what is called a plumb line. If a 
plummet hangs so that its point touches the 
surface of a vessel of water, the line and 
the surface of the water will be at right 
angles to each other, Fig. 25. The direc- 
tion of the line at any place is called the 
vertical, and a line at right angles to it is 
called a horizontal line. If vertical lines are 
drawn at different places on the earth, they 
will all be directed toward the earth's center. 

Hence, the direction of ter- 
restrial gravity is toward a 
point at or near the center 
of the earth, Fig. 26. At 
places near each other 
these verticals may be 
V" considered as parallel. 

80. The center of 

gravity is the point about 

which all the parts of a 

body balance each other. 

Each particle of a body is 

drawn toward the earth's 

center by gravity, and, hence, the effect of gravity on a 

body, taken as a whole, will be the same as the resultant of 

(50} 




yttft 



Fig. 26. 



EQUILIBRIUM. 



51 



an infinite number of equal and parallel forces. If we sus- 
pend a body so that it will hang freely from a point, a 
plumb line attached to the same point will show the direc- 
tion of this resultant. Now, on repeating this experiment, 
after suspending the body from another point, a second 
resultant will be found, and the center of gravity will be 
the common point of intersection of any two resultants. 

81. When the center of gravity is supported, the body 
will remain at rest. Hence, (1) the weight of a body may 
be considered as concentrated in the center of gravity ; or 
(2) the center of gravity may be regarded as the point of 
application of the force of gravity, since 
it is the only point common to all the 
resultants. The line of direction of a 
body w T ill be the vertical passing through 
the center of gravity, Fig. 27. 

82. Although a body will remain 
at rest, or in equilibrium, when its center 
of gravity is supported, this equilibrium 
may be one of three kinds : 

(1) A body is in stable equilibrium if it 
tends to return to its original position 
after it has been somewhat displaced. 
This will always be the case when any change of position 
elevates the center of gravity. A plumb line, when disturbed, 
finally comes to rest in its original position. 

(2) A body is in neutral equilibrium when it remains at rest 
in any adjacent position after it has been displaced. This 
will be the case when the point of support coincides with 
the center of gravity, as when a wheel is suspended on 
its axle. 

(3) A body is in unstable equilibrium when it tends to 
depart further from its original position after it has oeen 




Fig. 27. 



52 



ELEMENTS OF PHYSICS. 



slightly displaced. This will be the case when the paint of 
support is below the center of gravity. Thus, in Fig. 28, the 
cone B is in unstable equilibrium. It may be balanced in 
this position, but the least displacement will throw the 




Fig. 28. 
line of direction beyond the point of support, and the cone 
will topple over. The cone A is in stable equilibrium, be- 
cause its center of gravity is as low as it can be. The cone 
is in neutral equilibrium, because if it is rolled around 
the center of gravity will not be 
raised or lowered. 

The toy shown in Fig. 29 is in 
stable equilibrium, although the fig- 
ure without the balls would be un- 
stable. The addition of the balls has 
the effect of throwing the center 
of gravity below the point of sup- 
port. The same principle is illus- 
trated in Fig. 30. A pail is sus- 
pended from a stick lying on the 
edge of a table, and a second stick, 
EG, is placed with one end against 
the corner of the pail, and the other 
in a notch cut in the horizontal 
stick CD. By this contrivance the 
center of gravity of the connected bodies is brought under 
the edge of the table, and the whole is in stable equilibrium. 




Fig. 29. 



STABILITY. 



53 



The pail may now be filled with water without changing the 
equilibrium. 








Fig. 31. 



Fig. 30. 

83. The relation which gravity bears to equilibrium 
may be shown by the apparatus represented in Fig. 31. It 
consists of a cork, through which have been thrust, at right 
angles to each other, two 
half knitting needles and 
one whole one, and sup- 
ported by two wine-glasses - 
placed under one of the 
shorter needles. By push- 
ing the vertical needle up 
and down, the position of 

the center of gravity can be altered at pleasure, and the 
apparatus brought into either stable or unstable equilibrium. 
This is a case of a body resting on two points. A man on 
stilts is another — when at rest, he can be only in a state of 
unstable equilibrium. A man walking on a tight rope uses 
a long pole, which he thrusts from side to side to assist him 

1 in keeping the center of gravity vertically over the rope. 
A person walking on the thin edge of a plank, throws out 
his arms for the same reason. 

84. The stability of a body depends on the relation 
which the center of gravity bears to at least three points 
not in the same straight line, and on which it is supported. 



54 



ELEMENTS OF PHYSICS. 



The base of a body is the polygon formed by connecting the 
points of support ; as, for example, the legs of a table. 

A body resting upon a base is stable, when the line of 
direction falls within the base. The stability of bodies may 
be estimated by the force required to overturn them. This 
will be the force required to raise the entire body to the 
height that the center of gravity would be elevated in order 
to bring the line of direction beyond the base. 

The diagrams in Fig. 32 represent sections of different 
solids drawn through the center of gravity, G. To turn 




E E 

Fig. 32. 
any of these bodies over the edge E, the center of gravity 
must be raised through the height HT. A careful study of 
these figures leads to the following deductions : 

(1) The stability of bodies of the same height is increased 
by widening the base. The legs of chairs are inclined out- 
ward. A child's high chair has a very wide base. Candle- 
sticks and inkstands have broad bases. 

(2) The stability of bodies is increased by bringing the 
center of gravity to the lowest possible position. In load- 
ing a wagon or a ship the heaviest articles are placed at the 
bottom. A load of hay is easier overturned than a load 
of stone. 

(3) Of bodies having the same height and base, but of 
dissimilar figure, the pyramid is the most stable. 

Now compare the sections of the inclined figures in Fig. 
33, and, we may add, 

(4) The stability of a body is the greatest when the line 
of direction passes through the center of the base. 



MOVEMENTS OF MEN. 55 

(5) When the line of direction falls without the base, the 
body will fall, because the center of gravity is unsupported. 
The leaning towers in Pisa and Bologna incline far from a 
perpendicular position. In these the line of direction still 



I r, ,u 3 • 

Fig. 33. 
falls within the base ; but the visitor who sees them for 
the first time can not help thinking that they are likely 
to fall. 

85. Practical applications. — The center of gravity in 
man lies between his hips ; his base is the area inclosed by 
his feet. The different attitudes assumed by persons in 
standing or moving about are the results of instinctive efforts 
to keep the line of direction within the base. A man stand- 
ing with his heels against a vertical wall finds it difficult to 
stoop to the floor without falling forward. In running, or in 
climbing a hill, the body is thrown forward, so that its weight 
may be carried with less effort. In descending a hill, a man 
leans backward, so that his weight shall not cause him to 
fall forward. 

When a person carries a load, he endeavors to preserve 
the line of direction, common to himself and the load, with- 
in the base. If a heavy load is in the right hand, the body 
is inclined to the left, and the left hand thrown out. If the 
load is equally divided between his hands, or placed on his 
head, there is no tendency to lean to either side. If the 
load is on his back, he leans forward; if carried in his arms, 
he leans backward. 



56 ELEMENTS OF PHYSICS. 

Recapitulation. 

The center of gravity is the point in which the weight of the 
body may be considered as concentrated. 

Equilibrium is stable, neutral, or unstable, according to the posi- 
tion of the center of gravity. 

Stability depends on the relation which the center of gravity bears 
to the base. 



CHAPTER VI. 



THE LAWS OF FALLING BODIES. 



86. Gravitation has been shown to produce pressure; 
we are now to study how it acts in producing the motion 
of falling bodies. If we attempt to experiment by dropping 
different balls from a height, we shall meet with many 
difficulties. 

(1) The resistance of the air. Light bodies, as 
feathers and leaves, almost float in the air ; but if 
any two bodies whatever, as a coin and a feather, 
be made to fall through a perfect vacuum, they 
will reach the ground in exactly the same time. 
If two bodies have the same weight, but are of 
different material, as a lead bullet and a cork, the 
difference in bulk will make so great a difference 
in the resistance of the air as to make the cork 
fall perceptibly slower. If the bodies were of the 
same material, but of different size, the resistance 
of the air would be slightly in favor of the larger 
ball, although they would reach the ground in 
very nearly the same time. 

(2) If we catch equal balls, dropped from dif- fig. 34. 
ferent heights, we shall not only find that the swiftest balls 
are those which have fallen through the greatest heights, 
but that the velocity increases so rapidly that we can not 
readily measure the rate of increase in a free fall. There 
are several methods by which we may render the initial 
velocity so slow that it can be accurately measured. The 
simplest of these methods is that of Galileo, who first deter- 

(57) 



58 



ELEMENTS OF PHYSICS. 



mined the law of falling bodies by rolling smooth balls 
down a polished groove cut in a plane which he inclined at 
different angles of elevation. When a body rests upon an 
inclined plane, its weight or gravity is resolvable into two 
portions, one producing pressure on the surface, and the 
other tending to produce motion down the plane. This 
latter portion bears the same ratio to the whole force of 
gravity as the height of the plane does to its length ; and, 
hence, we may diminish the velocity of the ball at pleasure 
by lowering the height. Nevertheless, only the absolute 
motion will be changed ; the body will pass, in successive 
moments, through spaces bearing the same ratio to each 
other as if it fell freely through the air. 

87. To repeat the experiment of Galileo, stretch two 
parallel wires between the walls of a room, at any conven- 



I 

1 




Fig. 35. 
ient angle, as in Fig. 35. On the lower wire hang a weight 
to a pulley, so that it will move with little friction, and on 
the other fasten a convenient index, as a bell or a slip of 
paper, so that it may be struck by the top of the pulley b. 

Suppose that the inclination of the wire is such that, in 
the first second, the pulley passes over the space as; in the 
second, over the space ss f ; in the third, over s's"; and so on. 



LAWS OF FALLING BODIES. 59 

If we measure these spaces, taking that of the first second 
as unity, we shall find that they increase in the series of 
odd numbers — 1, 3, 5, 7, etc. — or at the rate of two spaces 
for each second. This proves that increase of velocity is 
uniform ; and that for bodies near the surface of the earth 
gravity is a constant force. 

Let us now see what we have gained by our experiment. 
(1) The spaces described by a falling body increase in the 
series of odd numbers — 1, 3, 5, 7. Any term of this series 
is equal to twice the number of seconds, minus one. 

First Law. — The space described by any falling body, in any 
given second, is equal to the product of twice the number of seconds, 
minus one, into the space described the first second. 

(2) The velocity is all the time increasing at the rate of 
two spaces for each second ; therefore we have the 

Second Law. — The velocity acquired by a falling body at the 
end of any given second is equal to the product of ilie number of 
seconds into twice the space described the first second. 

This product, it must be borne in mind, is the space a 
body would describe in the next second were gravity to 
cease to act, and not the space it actually describes. 

(3) The total space passed through at the end of the first 
second is 1 ; at the end of the second second, 1 -f- 3 = 4 ; at 
the end of the third second, 1 -f- 3 + 5 = 9. This series in- 
creases in the order of the squares of the number of seconds ; 
therefore we have the 

Third Law. — Tlie total space described by a falling body at 
the end of any given second is equal to the product of the square 
of the number of seconds into the space described ilie first second. 

It is evident that these laws are true, not only for any in- 
clination of the plane, but also for a free fall. If in the 
experiment the height of the plane had been one foot and 



60 ELEMENTS OF PHYSICS. 

the length sixteen feet, the pulley would have traveled in the 
first second, one foot ; in the second, three feet ; in the third, 
five feet, and so on. Therefore, a body falling freely 
through the air would pass, in corresponding time, through 
sixteen times these spaces; or, it would fall in the first 
second, sixteen feet ; in the second, forty-eight ; in the 
third, eighty, etc. 

88* It has been determined by careful experiment that, 
at the latitude of New York, a body will fall, in a vacuum 
through 16.08 feet in one second, and thereby acquire a 
final velocity of 32.16 feet. This last value is called the in- 
crement of velocity due to gravity, and is generally represented 
by g = 32.16. The space passed over during the first 
second is \g = 16.08.* 

89. The velocity increases every second by the quan- 
tity 32.16 feet. The velocity at the end of the first second 
is 32.16 ; at the end of the second, 64.32 ; at the end of the 
third, 96.48, and so on. Now, the total space fallen through 
at the end of the first second is 16.08 feet; at the end of 
the second, 64.32. feet; at the end of the third, 144.72 feet, 
etc. If we compare these two series we shall find that the 
velocity varies as the square root of the height fallen through ; for 

32.16 : 96.48 :: i/To\08 : 1/144772. 
This is an important law. The velocity which is acquired 



* We may employ formulee to express these laws by representing the 
space passed over during any second by 5; velocity by v; the total 
height of the fall at the end of any given second by $, and the num- 
ber of seconds by t. 

First law s=ig (2£ — 1). 
Second law v — tg. 
Third law S=lgt*. 



On combining these formulae v= ^2gS, t= V2S+ g, or VtS -*- 16.08, etc. 



PROJECTILES, 61 

by a body falling through any given height may be found 
by multiplying the square root of the height by \g, or by 
8.04. Thus, a velocity due to a fall of four seconds, or to 
a fall of (4 2 X16.08)=:257.28 feet, is 8.04 v ' 2508=128.64 
feet. 

90. If a body be thrown upward, the direction of the 
body is opposite to that of gravity, and, consequently, its 
velocity will be diminished each second by the quantity 
gr = 32.16. Hence, the time of ascent is the same as that 
of a falling body which attains a final velocity equal to the 
initial velocity of the ascending body. Further, if a body 
be projected upward, the height to which it ascends is such 
that when it falls again, the body will have acquired under 
gravity during its descent a velocity equal to that with 
which it started upward. 

91. Examples of this law. Suppose an iron ball is 
thrown upward with a velocity of 32.16 feet per second. 
At the end of one second it will come to rest and begin to 
fall. It will have moved in this second with an average 
velocity of (32.16 + 0) -v- 2 = 16.08 feet, and hence will rise 
to the height of 16.08 feet, 

Now, suppose the initial velocity be doubled, or 64.32 
feet. It will rise two seconds with the average velocity of 
(64.32 + 0) -r- 2 = 32.16, and will describe during the two 
seconds 32.16 X 2 = 64.32 feet, 

If the initial velocity be tripled, its average velocity will 
be (96.48 + 0) -- 2 = 48.24, and the total ascent 48.24 X 3 
= 144.62 feet. 

Hence, with a double velocity of projection it will rise 
four times as high, with a triple velocity, nine times as 
high, and so on. That is, the heights to which a body will 
rise are as the squares of the velocities of projection. 

In these examples the force has been doing work, for it 



62 



ELEMENTS OF PHYSICS. 



has carried the body through space in opposition to the 
constant force of gravity. Hence, the energy of the force 
is proportional to the square of the velocity. The energy is 
also proportional to the mass of the body, for it is evident 
that it requires twice the energy to raise two pounds that it 
does to raise one pound. Therefore, the energy is propor- 
tional to the mass multiplied by the square of the velocity. 

To compute the work done by a projectile force in oppo- 
sition to gravity, it is sufficient to multiply the weight of 
the body expressed in pounds by the number of feet through 
w T hich it is lifted. The height to which the body will rise 
is equal to v 2 -=- 64.32, or to the square- of the velocity divided 
by 2g. Hence, the work of the force, expressed in foot- 
pounds, equals mv 2 -r- 64.32. 

In general, the energy of a force is equal to one-half the 
product of the mass into the square of the velocity, or E = 

tjMV 2 . 

The factor j^rnv 2 is also called vis viva, or living force. It 
expresses the work that a moving body can perform before 
it is brought to rest, if no additional force is added to it ; as 
for instance, the power 
which different cannon 
balls would have to pen- 
etrate obstacles, like 
planks, clay, etc. 

92. If a projectile 
be fired in a horizontal 
direction, its path will 
be due (1) to the force 
of the gunpowder, and 
(2) to the constant force 
of gravity. In Fig. 36, 
suppose the velocity due to the powder to remain uniform 
during four seconds, and to be represented by equal spaces 





A 






B 


1 

3 


~\| 














I 


N 




5 


\ 








c 


\ 
\ 

\ 






\ 




7 


\ 


d 



Fig. 36. 



UNIVERSAL GRAVITATION. 63 

on the line AB, and represent the accelerating velocity due 
to gravity by, the unequal spaces 1, 3, 5, 7. The resultant 
of these two forces will be the curve Aabcd, which is called 
a parabola. 

93. Universal gravitation. Thus far we have considered 
gravity as acting only upon bodies near the earth's surface, 
and have found that for such bodies gravitation is a constant 
force proportional to mass. When we consider the earth's at- 
traction upon remote bodies, as the moon, or the universal 
gravitation acting between the heavenly bodies, we must 
take into account not only (1) the mass of each body, but 
also (2) the distance between the centers of gravity of the two 
bodies. The law of gravitation, discovered in 1666 by Sir 
Isaac Xewton, is usually stated as follows: 

Every particle of matter attracts every other particle, 
with a force (1) directly proportional to its mass, and (2) in- 
versely proportional to the square of its distance. 

Whenever the distance between any two bodies is consid- 
erable, gravity must be considered as a variable force which 
diminishes as the square of the distance increases. Thus, 
suppose a body taken one thousand miles above the earth's 
surface, it is five thousand miles from its center. The force 
of gravity will, therefore, decrease in the ratio of (f^o) 2 
= ^f. At this distance a body will weigh |4 of its surface 
weight, and during a fall of one second will acquire a velocity 
of ^f of 32.16 feet = 20.6 feet per second. At the distance 
of the moon, which is about sixty times the earth's radius, 
the attraction of the earth becomes (^V) 2 = awo"* an ^ 9 = 
.00892 feet. Hence, were the moon to fall toward the earth, 
it would pass in the first second over only .053 inch. 

94. The earth's equatorial radius is 13 \ miles longer 
than the polar radius, and we should expect from this that 
the force of gravity would increase in going from the equator 



64 ELEMENTS OF PHYSICS. 

toward the poles. This oblateness of the earth causes a gain 
of -g^ part of the weight of a body. The rotation of the 
earth on its axis causes another gain of -g-^g- part. The sum 
of these is yj^, which is the gain in weight that a body 
would experience on being carried from the equator to the 
poles. Consequently, the increment of gravity will vary 
with the latitude, being at the equator 32.0934 feet; at 
London, 32.1912; at Spitzbergen, 32.2528. 

Kecapitulation. 

Gravity is a constant force when mass alone is taken into account, 
but is a variable force when the distance between two bodies varies 
in a sensible ratio. It acts as a constant force on all bodies at the 
same place on the earth's surface and is a factor in the phenomena 
of pressure, of falling bodies, and of projectiles. 

Its intensity may be measured : 

(1) By the weight of bodies. 

(2) By the increment of velocity of falling bodies. 

(3) By the vibrations of a pendulum. 

A force may be measured (1) by the momentum or the inertia of 
moving bodies. (2) By the energy, or the power of doing w r ork. 

Problems. 

Suppose a body to fall freely in a vacuum: ,V* 

1. How many feet will it fall during the fifth second ? The sev- 
enth? The ninth? 

2. What will be its velocity at the end of the fifth second? The 
seventh? The ninth? t/ A *) . 

3. How far w T ill it have fallen at the end of the fifth second ? The 
seventh ? The ninth ? 

4. How many seconds will be required for a fall of 402 feet? Of 
578.28 feet ? /What will be the final velocity attained in these cases? ' 
What is the ratio between these final velocities? 1/1 

5. Suppose a body to be thrown upward with a velocity of 1029.12 
feet per second, to what height will it rise? How many seconds will 
elapse before it will come to rest? ^ 

/ ' - f.i^ 7 3 2. to ~ J 



CHAPTER VII. 



THE PENDULUM. 




Fig. 37. 



95. If a heavy weight or bob, as B, Fig. 37, be sus- 
pended from a point, A, by means of a fine string, it will 
be at rest only when in the line 
of the vertical A C. If the bob 
be raised to JB, it will tend to 
move through the curve B C, pre- 
cisely as a ball would roll down 
an inclined plane of the same 
height, HC. The force of gravity 
will be partially resisted by the 
string, and the remaining compo- 
nent of gravity will force the ball 
in the line BT. 

As the bob falls, it gradually gains in velocity, 
and, on falling the height H C, acquires sufficient 
momentum to carry it very nearly to D, an 
equal distance on the other side of the vertical. 
Thence it will return toward B, to repeat the 
vibrations until the resistance of the air shall 
bring it to rest. 

This may be considered a simple pendulum, 
which, by theory, has its weight concentrated 
in a single vibrating particle. The motion of 
the pendulum from B to D or from D to B is 
called a vibration. The laws of the vibration 
of the pendulum may be found, experiment- 
ally, by using simple pendulums of different 
lengths and weights, as shown in Fig. 38. 

(65) 




66 



ELEMENTS OF PHYSICS. 



96. The vibrations of a pendulum are caused by 
gravity alone ; hence, the time of vibration will not vary 
with the quantity or quality of the weight suspended. If 
the ball c be of copper and d of wood they will vibrate in 
the same time. Neither will the time of vibration vary to 
a sensible amount, whether the arc through which the bob 
passes be large or small, because any increase in the length 
of the arc is so compensated by the increased velocity of the 
fall, that the same pendulum will describe an arc of five 
degrees in about the time required for an arc of five min- 
utes. Hence : 

97. The time of vibration is dependent only on the 
length of the pendulum. If we make one pendulum, as a, 
one foot long, and another, as 6, four feet long, the first will 
vibrate in one-half the time of the other ; and if a third 
pendulum, c, be nine feet long, the first will vibrate in one- 
third of its time ; that is, the times of vibration of any two pen- 
dulums are proportional to the square roots of their lengths; and 
conversely, the lengths of any two pendulums are proportional to 
the squares of their times of vibration. 

At New York, a pendulum beating 
seconds is 39.1 inches long; a half sec- 
onds pendulum is 39.1 X (i) 2 = 9.78 
inches; of one vibrating once in three- 
fourths of a second is 39.1 X (f) 2 = 22 
inches. 

98. The compound pendulum con- 
sists of a heavy bob, suspended by an 
inflexible bar, from a fixed point, Fig. 
39. In this, the mass of the bob and 
the weight of the bar are both to be re- 
garded. In a rigid body, it is manifest 
that those particles nearest the point of suspension will 




COMPOUND PENDULUM. 67 

tend to vibrate in the shortest time. Hence, a particle at a 
will accelerate a more distant particle at b y and the more 
distant particles will retard those that are nearer the 
point of suspension. There will, however, be one particle, 
as at o, which moves at the average rate of all, in which the 
tendency of the particles above it to accelerate its motion 
is exactly compensated by the tendency of the particles be- 
low it to retard its motion. This particle will, therefore, 
move as if it were vibrating alone, suspended by a thread 
which had no weight, thus fulfilling the conditions of a 
simple pendulum. The position of this particle is called the 

center of oscillation. 
i 

99. The length of a compound pendulum is the dis- 
tance between the centers of suspension and oscillation. In 

1 a uniform bar, suspended from one end, the center of oscil- 
1 lation w T ill lie two-thirds of the length of the bar from the 
center of suspension. 

100. The centers of oscillation and suspension are 
mutually interchangeable. It is this fact which enables us 

; to determine the length of a seconds pendulum with accu- 
racy. We may obtain good results by the follow- pp, 
ing simple apparatus, Fig. 40. Make of hard ,„ 
wood a slender bar sixty inches long. Mark the 
position of the center of gravity, which should be 
made to correspond very nearly with the center of 

! the bar. About 39.1—2 = 19.55 inches above 

, and below this point insert two needles. 

The bar, made to vibrate from either needle, will 
vibrate in about one second. If the vibrations 
from the two centers are not performed in the same ^ I 

j time, the bar may be adjusted by elevating or de- W ! \ 
pressing the center of gravity. This may be done fig. 40. 
by placing a coil of fine wire about the bar, where patient 



\G' 



68 ELEMENTS OF PHYSICS. 

trial shall determine it is needed. When the times of vibra- 
tion are the same from either point of suspension, the dis- 
tance between them is the length of the pendulum. If the 
precise time of this vibration is known, as well as the length 
of the pendulum, the length of a seconds pendulum can be 
calculated. 

101. Suppose that we have found, in this bar, that S is 
the center of suspension and the center of oscillation, 
what effect will be produced on adding weights ? 

(1) All the matter of the pendulum may be considered 
as concentrated at 0. Hence, if we add a weight, W, at 
this point no change will be made in the rate of vibration, 
although the bar will have a new center of gravity, as at G\ 

(2) If the weight be applied below 0, as at W, the cen- 
ters of gravity and oscillation will both be depressed, and 
the length of the pendulum increased. 

(3) If the weight be applied between S and 0, as at W", 
its effect will be to raise the centers of gravity and oscilla- 
tion, and to shorten the pendulum. 

(4) If the weight be applied above S, as at W"\ it tends 
to retard the vibration of the bar, because the particles 
above S move in directions opposite to those below. The 
time of vibration is thereby lengthened, and, consequently, 
the center of oscillation lowered, while the center of gravity 
is raised. 

(5) If sufficient addition be made above S, the center of 
gravity may be made to coincide with the center of suspen- 
sion. The bar will then be in a state of neutral equilibrium, 
and if set in motion will tend to rotate continually. 

(4 and 5) Now, as we can raise the center of gravity as 
near the center of suspension as we please without making 
them coincide, Ave may so lower the center of oscillation 
that it shall be below the bar. The bar may be made to 



COMPENSATING PENDULUM. 



69 



vibrate in two, three, or even five seconds, which correspond 
to the vibrations of pendulums whose lengths are 156.4, 
351.9, and 977.5 inches. It is on this principle that the 
metronome is constructed. 

102. The principle of the pendulum was discovered by 
Galileo in 1581, but it was first employed in clocks by 
Huyghens, in 1656. The utility of a pendulum, as a meas- 
ure of time, depends upon the perfect equality in the times of 
its vibration. It is, therefore, essential that the distance 
between the centers of suspension and oscillation should be 
invariable. In ordinary clocks, heat tends to lengthen and 
cold to shorten the pendulum, and hence such clocks are 
apt to go too slow in summer and too fast in w T inter. Clocks 
are regulated by raising the bob to make 
the clock go faster, and by lowering the 
bob to make it go slow T er. 

103. Compensating pendulums are those 
which are self-regulating. They are made of 
two substances in such proportions that the 
change in length of one upward is exactly 
compensated by an equal change of the 
other downward. The gridiron pendulum, 
Fig. 41, consists of a series of five steel bars, 
expanding downward, and a series of four 
brass bars expanding upward. In this the 
length of the steel bars is - 1 -^ Q - that of the 
brass. The seconds mercurial pendulum, 
Fig. 42, has at the end of a steel rod a 
cylinder containing a column of mercury 
6.7 inches high. 

104. The mode in which the pendulum 
is applied to clocks is shown in Fig. 42. The pendulum 
rod passing between the prongs of a fork, /, communicates 




Fig. 41. 



70 



ELEMENTS OF rHYSICS. 



its motion to the rod, r, which oscillates on a horizontal 

axis, a. To this axis is fixed the escapement, PF, terminated 

by two projections, or pallets, which 

work alternately in the teeth of the 

scape wheel, S. This wheel, acted on 

by the weight, W, through a train of 

wheels (not shown in the figure), tends 

to move in the direction of the arrow r . 

If the pendulum is at rest, the wheel 

is held at rest by the pallet, P', and 

with it all of the clock work. 

Now, if the pendulum be moved to 
the position shown by the dotted line, 
P is raised, and the wheel escapes from 
the pallet, and the weight causes the \ 
wheel to turn until its motion is ar- < 
rested by the other pallet, P', whicli Fig. 42. 

has been brought in contact with another tooth of the wheel 
in consequence of the motion of the pendulum. In this 
manner the descent of the weight, and the consequent move- 
ment of the clock-work is regulated by the pendulum. The 
faces of the pallets are slightly inclined, so that each tooth 
of the wheel, on escaping, gives the escapement a slight 
impulse, which is communicated to the pendulum, and com- 
pensates for its loss of motion, due to friction and the resist- 
ance of the air. 




105. Since the length of the seconds pendulum can 

be determined with great accuracy, we may use it as a 
means of determining the variation in the intensity of 
gravity on the earth's surface. The length of the seconds 
pendulum at the equator is 39.02167 inches; at New York, 
39.10237 inches; at London, 39.13983 inches; at Spitsber- 
gen, 39.21614 inches. The same pendulum would, there- 



PENDULUMS. 71 

fore, vibrate in less time on being carried from the equator 
to the poles. Now, as the fall of the pendulum is due to 
gravity, the lengths of any two pendulums in different lati- 
tudes, which have the same time of vibration, are directly 
proportional to their increments of gravity. * 



* The time of vibration of a pendulum is expressed by the formula 

? = 3.1416 Vi -4- g : if t be one second, then, at New York, g = 9.Sll % or 

gr = 39.10237 X 9.87 =385.94 inches. The fall of a body during the 

'first second, in vacuo at New York, is one-half this quantity, or 192.97 

inches. 

Kecapitulation. 

The pendulum may be simple or compound. 

The length of a pendulum is the distance between its centers of 
suspension and oscillation. 

The time of one vibration depends, 

(1) On the force of gravity. 

(2) On the length of the pendulum. 

(3) It is not sensibly influenced by the material of which it is 
made, nor by the arc through which it vibrates, excepting when 
these arcs are very unequal. 

Problems. 

1. What is the length of a pendulum making one vibration in 
four seconds? In one-fourth of a second? In eight seconds? In 
one-eighth of a second? 

2. What will be the time of vibration of a pendulum thirteen feet 
long? Thirty inches long? 

3. Suppose a seconds pendulum loses one minute a day, should it 
be lengthened or shortened? How much change is required? 



d 



CHAPTER VIII. 

SIMPLE MACHINES. 

106. A machine is an instrument by means of which a 
force, applied at a certain point, tends to produce motion at 
another point, more or less distant. The force employed in 
a machine is called the poiver. The resistance which is over- 
come by a machine at the point where the power acts, is 
called the weight or load. 

107. Among the many advantages derived from the 
use of machines are : 

(1) They enable us to utilize the products of nature. It 
is the knowledge of machinery that marks civilized- life, 
since by it we have mills for weaving cloth, grinding flour, 
forging iron, etc. 

(2) They enable us to employ other forces than our own, 
as the strength of animals, the forces of wind, water, and 
steam. 

(3) They enable us to employ our full strength at one 
time. A person winding thread on a reel expends but a 
small portion of his strength ; with suitable machinery he 
can turn many reels at the same time. 

(4) They enable us to change the direction of our force. 
A sailor may hoist the sails of a ship while standing on 
deck, instead of pulling them up after he has climbed the 
mast. 

(5) They enable us to perform work that we could not do 
with our unassisted strength. By using a crow-bar, a man 
may raise a large stone, which he could not stir with his 
hands. 

(72) 



MACHINES. 73 

108. No machine can create force. It is merely an 
inert instrument for the advantageous application of force. 
In fact, part of the force applied to machines is expended 
in overcoming friction, the resistance of the air, and in lift- 
ing the parts of the machine ; hence, only a part of the 
force is effective in doing useful work. In the theoretical 
study of machines, these items are neglected, and it is gen- 
erally assumed that no force is lost in the machine. 

109. The work of the power is equal to the work of the 
load. If any machine enables us to lift a weight of ten pounds 
by the power of one pound, (1) the power must move ten 
times the space traversed by the load ; (2) as the spaces are 
traversed in the same time, the power must move ten times 
as fast as the load. Conversely, if a power of ten pounds is 
required to move a weight of one pound, (1) the load will 
traverse ten times the space, and (2) with ten times the 
velocity of the power. The law of virtual vebcities is an ex- 
pression of these facts. It also receives a concise expression 
in the axioms, 

" What is gained in power is lost in velocity ; 
What is gained in velocity is lost in power." 

110. All machinery may be comprised in six elementary 
forms, called simple machines. These are (1) the lever, (2) 
the wheel and axle, (3) the pulley, (4) the inclined plane, 
(5) the wedge, (6) the screw. We shall study only the 
most important varieties* of these. 

111. A lever is an inflexible bar, moving freely about a 
fixed point, which is called a fulcrum. The arms of the 
lever are the parts into which the fulcrum divides it. 

There are three classes of levers w T hich are represented in 

Fig. 43. In levers of the first kind, the fulcrum is between 

the power and the load. In -levers of the second kind, the 

load is between the power and the fulcrum. In levers of 
Phys. 7. 



74 



ELEMENTS OF PHYSICS. 



the third kind, the power is between the load and the 
fulcrum. 

112. Familiar illustrations. 
A crow-bar is a lever of the 
first kind when we press one 
end downward to raise a load 
above a block used as a fulcrum, 
Fig. 44. It is a lever of the 
second kind, when one end rests 
on the ground as a fulcrum and 
we raise the other end upward 
to lift the load, Fig. 45. A 
fishing rod is a lever of the 
third kind; the fish being the 
load, the power is applied by one hand, while the other hand 
at the end of the rod acts as the fulcrum. The hinges of a 




Fig. 43. 




Fig. 44. 




door are its fulcra; the load is at the center of gravity of 
the door ; in closing it, it is a lever of the second kind, when 
the hand is applied near the latch ; but a lever of the third 
kind when the hand is near the hinges. 

Since the work of the power is equal to the work of the 
load, the power multiplied by the vertical distance through 
which it passes equals the load multiplied by the vertical dis- 
tance through which it passes. This law applies to all 
machines, but we can give it another expression, of greater 
convenience for each simple machine. Thus : 

113. The law of the lever. The product of the powerful 



LEVEES. 75 

tiplied by its distance from the fulcrum is equal to the product of 
the load multiplied by its distance from the fulcrum. 

That is, using the letters in Fig. 43 : 

p x FF= L x IFF. 

This law is called a statical law, because it expresses the 
relation of the power to the load when a machine is in ex- 
act equilibrium. To produce motion it is necessary that 
this equilibrium should not exist, which will be the case 
when one product exceeds the other. The machine will 
then move in the direction of the greater product. 

Examples. In a lever of the first kind, sixteen inches 
long, with the fulcrum four inches from the load, and, 
therefore, twelve inches from the power, a power of one 
pound will balance a load of three pounds. Now, if an 
ounce be added to the power it will raise the load ; if it is 
added to the load, the power will be raised. 

In a lever of the second kind, sixteen inches long, with 
the load four inches from the fulcrum and the power six- 
teen inches, a power of one pound will balance a load of 
four pounds. 

In a lever of the third kind, sixteen inches long, with the 
power four inches from the fulcrum, a power of four pounds 
will balance a load of one. 

If we wish to prove these by actual experiments, we must 
first balance the lever by a sufficient counterpoise, before 
attaching the power and the load. 

114. Levers of the first and second kinds are generally 
used to move heavy weights w T ith small powers. Their effi- 
ciency may be increased (1) by increasing the power ; (2) by 
increasing its relative distance from the fulcrum. Levers 
of the third kind are used when we wish to move small loads 
with great velocity by the use of great powers. We may 
also employ levers of the first kind for the same purpose. 



76 



ELEMENTS OF PHYSICS. 



115. When a beam rests on two props and supports a 
weight between them, the amount supported by either prop 
may be estimated by 
considering it as the 
power and the other 
prop as the fulcrum. If 
A and B carry a weight 
between them on a pole, 
each man will bear half 
the burden if the weight 
hangs from the middle 
of the pole. In all other 
cases, the load sustained 
by each increases as the 




Fig. 46. 



distance between him and the load decreases. For example : 
if the weight is one-third the length of the pole from A, he 
will bear two-thirds of the burden and B one-third. Two 
horses attached to a wagon may be made to pull unequal 
loads by placing the bolt of the whipple-tree nearer the 

stronger horse. 

116. When a small force 

is required to sustain a consid- 
erable weight, and it is not 
convenient to use a long lever, a 
combination of levers, called a 
compound lever, may be em- 
ployed. 

A compound lever is shown 
in Fig. 47. A F is a lever of 
the second kind; the power, 
P, acting at A produces a 
downward force at B as many 
times greater than itself as the distance A F is greater than 




BALANCES. 



77 



B F. This effect is then transmitted as a power at A', which 
will tend to raise B' upward, with a force as many times 
greater than itself as A'F' is greater than F'B'. Finally, 
the effect at B' will be a new power when transmitted to A", 
and will tend to lift the load at JB", with another increase 
of effect. If these levers are so arranged that the power 
arm in each is ten times as long as the load arm, a power 
of one pound at P will balance a load oflOxlOXlO = 
1,000 pounds at L. 

When a compound lever is at equilibrium, the power multi- 
plied by the continued product of the alternate amis, commencing 
with the power, equals the load multiplied by the continued prod- 
uct of tlie alternate arms, commencing with the load. 

117. The practical applications of the lever are very 
numerous. The balance is a lever of the first kind, having 
two equal arms. Delicate balances have a small needle at- 




FlG. 48. 

tached to the center of motion, which oscillates before an 
index, n, to show very small deviations of the beam. 

A balance is sensitive, when a very small difference be- 



78 ELEMENTS OF PHYSICS. 

tween the weights causes a perceptible motion in the pointer 
It must be in a state of stable equilibrium; that is, the 
center of gravity should be below the fulcrum, but not too 
far, because it will require too great a force to set it in 
motion. The apparatus of Fig. 31 well illustrates this ; the 
horizontal needle will be the most sensitive to a small addi- 
tion of weight, when the vertical needle is so placed that 
the center of gravity of the apparatus is a very little below 
the axis of suspension. 

The arms of a balance must be equal in length, otherwise 
one will have a greater leverage than the other, and un- 
equal weights will be required to produce equilibrium. To 
test this, place weights in each scale pan and bring the 
beam to a horizontal position. Now transfer the weights to 
the opposite scale pans. If the beam remains horizontal, the 
arms are equal. 

118. Dishonest dealers are said to use balances with 
unequal arms, placing their merchandise when buying in the 
shorter arm, but when selling in the longer. The true 
weight of the merchandise is the square root of the product . 
of the false weights. That is, if a body requires nine pounds 
to balance it from one side and four pounds from the other, 
the true weight is six pounds.* 

119. The wheel and axle consists of a wheel and cylin- 
der firmly united and free to revolve on a common axis. 
The power is applied at the circumference of the wheel and 
tends to move a load applied at the circumference of the 
cylinder or axle. This machine acts continuously as a lever 



*When_a body whose true weight is iv is in C, let it be balanced 
by a: pounds in E. When in E, by y pounds in C, and let A and B 
be the lengths of the arms. Then, 

ivA = xB and wB — yA. Multiplying these together w 2 AB = xyAB. 
Dividing by AB, w^—xy. w—\/xy. 



WHEEL AND AXLE. 



79 



of the first kind, the fulcrum being at F, the common cen- 
ter, the arms of the lever being AF and FB, 
the radii of the wheel and axle. Hence, the 
power multiplied by the radius of tlie wheel equals 
the load multiplied by the radius of tlie axle. That 




is, PyiAF^LxBF. 

Example. When the wheel is six feet in ra- 
dius and the axle six inches, a power of one 
pound will balance a load of twelve pounds. 

120. In the various forms of this machine, the load is 
generally attached to a rope w T ound round the axle; the 
power is applied in several different w T ays. 

The form represented in Fig. 49 is that used in ware- 
houses, in which the power is applied by means of a rope 
coiled on the wheel. When the rope on the wheel is un- 
wound, that on the 
axle is wound up, 
and the load raised. 
The power may also 
be applied to pins 
projecting from the 
wheel, as in the steer- 
in g apparatus on 
large vessels. 

It is not necessary that the power be applied to a complete 
wheel, since a single spoke will answer. 
The winch of the common windlass, 
Fig. 50, is such a spoke for the appli- 
cation of the power. In the windlass 
used on ships, the winch is replaced 
by handspikes w T hich fit into slots cut in 
the axle, and are shifted as occasion requires. The capstan, 
Fig. 51 , is a vertical windlass, turned by men walking around 
it and pressing against handspikes inserted in the top or drum. 




Fig. 50. 




Fig. 51. 



80 



ELEMENTS OF PHYSICS. 



121. The power of this machine may be augmented on 
the principle of the compound lever, by combining several, 




Fig. 52. 



so that the axle of the first may act on the wheel of the 
second, and so on. These are frequently connected by 




Fig. 53. 

means of cogs, as in clock-work; or by means of endless 
bands of leather, as in turning lathes. 

122. The pulley. Suppose a cord, fastened at one end 
to a hook, supports a load at the other end. The tension 



THE PULLEY. 



81 




Fig. 54. 



of the cord will be transmitted throughout its whole length, 
and exert a force on the hook equal to the weight of the 
load. If the cord be passed over the hook and one end 
held by the hand, the tension of the cord will be the same, 
and the hand must exert a force equal to the load. If we 
pull up the weight by the hand, we 
shall gain no mechanical advantage ex- 
cept a change in the direction in which 
the power acts. In fact there will be a 
loss, due to the friction of the cord upon 
the hook. We may diminish the friction 
by passing the cord over a wheel revolv- 
ing on the hook as its axis, but can not 
lessen the tension of the cord. A pulley 
is a small grooved wheel revolving about an axis, and hav- 
ing a cord passing over its circumference. If the axis is 
fixed, the pulley is a fixed pulley : if the axis is movable, the 
pulley is a movable pulley. 

123. In the fixed pulley the power and load are equal. 
The advantage derived from its use is merely a change in 
the direction of the power. Thus, if a fixed pulley be at- 
tached to the rafters of a house, a man standing on the 

ground may raise loads to any floor 
of the building. As it is easier 
for him to pull the rope down than 
it would be to lift the weight di- 
rectly upward, he can also afford to 
overcome the friction of the pulley. 
By the use of two fixed pulleys, as 
in Fig. 55, horizontal motion may 
be converted into vertical. 

124. Movable pulley. If a cord be fastened at each end 
to a hook and a load hung by a ring in the middle of the 




Fig. 55. 



82 



ELEMENTS OF PHYSICS. 



cord, the weight of the load will be distributed ; that is, each 
half of the cord will support but half 
the load. Therefore, if a fixed pul- 
ley take the place of one of the 
hooks, the power required to support 
the load will be one-half of the 
weight of the load. If it is desired fig. 56. 

to elevate the load, a movable pulley may be substituted for 
the ring in order to have less friction, as in Fig. 57. 

If one end of the cord be attached to the top 
of the movable pulley, as in Fig. 58, the tension 
due to the load will be distributed in three equal 




T 




Fig. 57. 



Fig. 58. 



Fig. 59. 



parts. Consequently the tension of the part of the cord to 
which the power is applied will be one-third of the load, 
and the combination will be in equilibrium when the power 
is one-third of the load. In the arrangement of Fig. 59, 
the power is one-fourth of the load. 

125. As fixed pulleys do not increase the power, the 

gain in the last three examples must be due to the distribution 
of the tension among the parts of the rope supporting the 
movable pulley. Hence, the load equals the power multiplied 



INCLINED PLANE. 



83 



by the number of parts of the cord engaged in supporting the 
movable pulley* 

126. The inclined plane is a hard, smooth, inflexible 
surface, inclined to the horizon. When a load is placed on 
a horizontal plane, the whole weight is supported by the 
plane : if the plane is tilted, a portion of its weight tends to 
make the load slide or roll down the plane. Thus in Figs. 60 




Fig. 60. 



and 61, the weight of the load lies in the direction of gravity, 
LG: this may be resolved into two components, one, L N, 
pressing upon the plane and perpendicular to it ; the other, 
L E, which must be counterbalanced by the application of 
power, to prevent the load from sliding down the plane. 
The steeper the plane, the greater will be the power required. 
We shall consider two cases. 

(1) When the power acts parallel with the plane, as in 
Fig. 60, L E represents the power required, and L G, or its 
equal, EN, the weight of the load. The triangles, LEN 
and ABC, are similar, and L E will bear the same relation 
to E N that B C does to A C; that is 

Power is to load : : LE : EN, or : : BC to AC. 

Hence: the power equals the load multiplied by the ratio of Hie 
vertical height of Hie plane to its length. 

Thus, the power required to keep a barrel weighing two 



* The law supposes that there is but one cord, and that its parts 
are parallel to each other. 



84 



ELEMENTS OF PHYSICS. 



hundred pounds on a plank twelve feet long, with one end 
on the ground and the other on a wagon three feet high, 
will be 200 X T \ = 50 pounds. 

This is the most advantageous way of applying the power, 
because its whole effect is expended in raising the load. 

(2) When the power acts parallel with the base, as in 
Fig. 61, a part of the power is expended in increasing the 
pressure on the plane, and we shall find, 

Power is to load :: LE : EN, or :: BC : AB. 
Hence: the power equals the load multiplied by the ratio of the 
vertical height of the plane to its base. 

127. Familiar examples are found in roads, which are 
seldom perfectly level. On a level road, the power of a 
horse drawing a wagon is expended in overcoming friction. 
On a road rising one foot in twenty, the horse must lift 
one-twentieth of the load besides overcoming the friction. 
If we reckon friction at one-eighteenth of the weight of the 
wagon and its contents, the power necessary (^ -f -Jg-) will 
be almost double that required on a level road. Hence, in 
ascending mountains the road winds about so as to increase 
the length of the incline. 

128. The wedge is a movable inclined plane. If, instead 
of moving the weight along the inclined plane, Fig. 61, the 
plane had been pushed under the load, the same advantage 
would have been gained. Therefore, since 
in the wedge, the power is always exerted 
parallel to the base, the power is to the load 
as the height of the wedge is to the base. 

129. The double wedge, as Ac A', is the 
form generally used. As each face meets 
half the resistance, the power is to the re- 
sistance as half the thickness of the w T edge 
is to its length, B c. 




JBlG. 62. 



THE SCREW. 85 

This law is of little practical use, beyond the general de- 
duction that the efficiency of the power increases with the 
thinness of the wedge ; because, 

(1) The power is applied, not by a continuous force or 
pressure, but by percussion, and in such a form that we can 
not give it a numerical value. 

(2) The surfaces to be separated generally assist the 
action of the wedge, by their elasticity at the moment of 
impact, and sometimes by the leverage of the faces to the 
cleft. 

(3) The value of the wedge is often entirely dependent 
on friction, as is the case with nails, and the key-stones of 
arches. 

130. The wedge is used where very great force is to be 
exerted through a small space. Masses of stone and timber 
are cleft by wedges. Ships are raised when on the stocks 
by wedges driven under their keels. Knives, awls, hatchets, 
chisels, and other cutting instruments, are wedges. 

131. The screw is another variety of the inclined plane, 
as may be shown by winding a triangular piece of paper 
around a cylinder. The hypotenuse will form a spiral path 
exactly resembling the thread of a (% * 
screw. The vertical distance, as 6 c, 
between two threads represents the 
height of the plane, and the circum- 
ference of the cylinder the base of , 
the plane. The power acts parallel f|^^j|)jip 

to the base, as in the second case of fig. 63. 

the inclined plane. Hence, 

The power is to the load as the vertical distance between two 
adjoining threads is to the circumference of the screw. 

132. In actual practice, the screw consists of two parts, 



ELEMENTS OF PHYSICS. 




Fig. 64. 



(1) a convex grooved cylinder, or screw, S, which turns 
within (2) a hollow cylinder or nut, N, whose concave sur- 
face is cut with a thread exactly 
corresponding to the threads of 
the screw. The power is em- 
ployed either to turn the screw 
within an immovable nut, or to 
turn the nut about a fixed screw. 
In both cases, it is generally ap- 
plied by means of a lever. This 
renders the contrivance a com- 
pound machine, whose advantage may be found by the fol- 
lowing law : 

The poiver is to the load as the vertical distance between two 
adjoining threads is to the circumference described by the power. 
Power is to load :: be : 2tt7P, or :: be : 6.2832 TK 
Example. If the threads of the screw are one inch apart, 
and the lever is four feet long, a power of five pounds will 
exert a pressure of 4 X 12 X 2 X 3.1416 X 5 = 1507.97 
pounds. 

133. The screw is used for compressing cotton and hay, 

for expressing the 
juices of plants and 
fruits, for raising 
buildings, for propel- 
ing ships, and for 
many minor pur- 
poses. 

134. Compound 

machines are combi- 

Fig. 65. nations of two or more 

simple machines. One of the most useful of these is the 

endless screw, Fig. 65; its thread works obliquely into the 




HUMAN MECHANISM. 



87 




teeth of a wheel, which supplies the place of the nut. 
Cranes and derricks are combinations of pulleys with the wheel 
and axle. The crane shown in 
Fig. 66 has a wheel and axle at 
G, two fixed pulleys, F and E, 
and one movable pulley, P. The 
mechanical advantage of a com- 
pound machine is found by esti- 
mating the effect of the parts 
separately and then multiplying 
these together. 

135. The human mechanism 
exhibits many examples of sim- 
ple machines. Fig. 66. 

Thus, the nodding of the head illustrates a lever of the 
first kind, in which the load is the weight of the head; the 
fulcrum, the atlas bone ; and the muscles of the neck, the 
power. When a man stands on his toes, the floor is the 
fulcrum; the power is applied at the heel by the tendon 
Achilles; and the weight of the body falls between the ful- 
crum and the power. This is a lever of the second kind. 

We employ a lever 
of the third kind in 
raising the fore-arm. 
The hand, and any 
thing that it contains, 
is the weight; the el- 
bow-joint, the ful- 
crum ; and the power is applied by a muscle attached to the 
fore-arm a little in front of the joint, Fig. 67. In biting by 
the front teeth, we employ a lever of the third kind. The 
force exerted by the muscles which raise the lower jaw is 
enormous. In man it can not be less than three hundred 




Fig. 67. 



88 ELEMENTS OF PHYSICS. 

pounds, and in the tiger it must exceed two thousand 
pounds. The muscle which directs the eye downward and 
inward, passes through a cartilaginous pulley attached to the 
frontal bone. Some of the teeth are wedges, capable of 
cutting like chisels. 

Throughout the entire frame we have surprising examples 
of economy of material to the end designed ; combining 
lightness, force, firmness, elasticity, leverage, motion, resist- 
ance, security, and grace. These contrivances are so numer- 
ous, and so wonderfully constructed, that a volume would be 
insufficient to describe them. 

Recapitulation. 

Machines are simple or compound. 



Simple machines 
employ 



f Lever, 

1. Leverage, j wheel and axle 

2. Tension of ropes, Pulley. 

{Inclined plane, 
Wedge, 
Screw. 
Machines are compounded (1) by repeating the same simple machine, 
as the compound lever; (2) by uniting two or more simple machines, 
as the crane. 

> Problems. 

1. Suppose a power of 50 pounds moves through a vertical dis- 
tance of 10 feet, how high can it lift a load of 250 pounds? How 
great a load can it lift 100 feet high ? In each case what will be the 
relative velocities of the power and the load? 

2. A power of 75 pounds is applied at one end of a lever 12 feet ._ 
long to move a load at the other end; what will be the load when 
the fulcrum is at the center of the lever? When the fulcrum is 3 
feet from the load? 1 foot from the load? 

3. When the same bar is employed as a lever of the second kind, 
what will be the load when it is sustained at the center? At 3 feet 
from the fulcrum? At 1 foot? : 



/ 



PROBLEMS. 89 

4. If, with the same bar, the load and the fulcrum be placed at 
the ends and the power applied between them, what will be the load 
when the power is at the center? At 3 feet from the fulcrum? At j S 
1 foot? 

5. If, with the same bar, a power of 30 pounds balances a load of 180 
pounds, how far from the load will the fulcrum be when it is used 
as a lever of the first kind? As a lever of the second kind? 

6. If A and B carry between them, on a pole 9 feet long, a load 
of 150 pounds, how much will A bear when the load is 3 feet from 
him? 6 feet? 

7. In the compound lever, shown in Fig. 47, A F is 6 feet long, 
A'B' 4 feet, A" F" 5 feet, and the distances FB, F' B', F" B", each 
1 foot, what is the relation between the power and the load ? What 
load may be sustained by a power of 60 pounds? 

8. In a false balance, a bundle weighs 16 pounds in one scale pan 
and 9 pounds in the other, what is the true weight? >^ T hat isthe^ 
relative length of the arms? Prove the answers obtained, j ^"N 

9. In a wheel and axle, the radius of the wheel is 10 feet and that 
of the axle 6 inches; required, the load that may be sustained by a 
power of 1 pound? By 100 pounds? 

10. With the same machine, what will be the length of the rope 
unwound from the wheel, when the load has been lifted 10 feet? 

11. A capstan has an axle one foot in diameter, and is furnished 
with 5 handspikes, each 6 feet long; how much power must be ap- 
plied at each handspike to lift an anchor weighing 4,000 pounds? 

12. In a wheel and axle, the axle is 8 inches in diameter, and is 
turned by a winch of 2 feet radius ; what is the load that may be 
lifted by a power of 100 pounds? What is the power required for 
100 pounds? 

13. In a train of 3 wheels, the number of teeth in each wheel is 
64, the number of leaves on each pinion 16: when a power of 10 
pounds is applied at the circumference of the first wheel, what load 
will be sustained at the third pinion ? How many times must the 
first wheel revolve in order that the third pinion be turned around 
once? 

14. In a system of 2 movable pulleys, with a continuous cord, the 
power is 100 pounds; required, the load. 

PHVS. 



90 ELEMENTS OF PHYSICS. 

15. On a road rising 1 foot in 25, what power will be required to 
sustain a wagon weighing 1,000 pounds? If A // 

16. In a book-binder's press, the lever is 6 feet long, and the threads 
of the screw 0.5 inch apart ; what pressure may be applied by a power 
of 100 pounds? 

17. If 12 turns of a screw carry the head forward 1 inch, what 
power, applied to a lever 6 feet long, is required to exert a pressure 
of 2000 pounds? 

18. In the crane, Fig. 66, the axle at G is 6 inches in diameter, 
and the winch 3 feet in radius, with one movable pulley ; what will 
be the relation between the power and the load? The wheel and' 
axle remaining the same, what advantage may be gained by the use/ / 
of a system containing four movable pulleys? / ' 



(m 



■37.19 ?&JiSi 

. ^ * Tt 



y/^riWr 



*y£ 



CHAPTER IX. 



FLUIDS AT REST. 



136. Solids act in masses; if we move one end of a stick 
the whole stick will be moved, by reason of the coherence 
of its molecules. The molecules of fluids act independently 
of each other, and hence will move on the application of a 
very small force. 

137. Liquids and gases are governed by very nearly 
the same laws. The principal difference between them arises 
from the fact that gases are easily reduced in volume by 
pressure, while liquids may be considered as non-compressible 
fluids. The pressure of one atmosphere causes in water a 
decrease of only 0.00005 part of its original volume, and in 
mercury only 0.000005 part. As soon as the pressure is 
removed both liquids and gases return to their original 
volume, showing that they are both perfectly elastic. The 
energy of the elasticity with which they resist a force that 
compresses them is exactly equal to the compressing force. 

138. Solids transmit pressure only 
in the direction of the force acting 
upon them. Liquids transmit pressure 
undiminished in every direction. This fact 
may be demonstrated by experiment. 
Take a vessel of any shape, in whose 
sides are cylindrical apertures closed 
by movable pistons, whose areas are, 
respectively, 1, 2, 3, 4, and 5 square 
inches, and fill the vessel with water so that it shall be 

(01) 




Fig. 68. 



92 ELEMENTS OF PHYSICS. 

completely closed in on all sides. Suppose the water to 
have no weight and the pistons no friction, or, what amounts 
to the same thing, suppose the friction is equal to the 
weight of the water, then there will be no tendency to 
motion anywhere in the vessel. Now apply a pressure of 
one pound upon the piston w T hose area is one square inch. 
Each molecule beneath the piston will be slightly com- 
pressed, and develop a corresponding elastic force in each. 
Each one w T ill then react upward against the piston, down- 
ward against the molecules beneath, and sideways against 
the adjoining molecules, or against the sides of the vessel. 
The next tier of molecules will transmit the pressure in the 
same way to a third tier, and they onward, until every 
molecule both receives and transmits an equal pressure. 
Therefore, each piston will be thrust outward with a force 
proportional to the number of molecules beneath it, and, as 
these are of the same size, the pressure on each piston will 
be proportional to its area. It will require a pressure of 
two pounds to keep a piston of two square inches in place; 
three pounds for one of three square inches, etc. Any por- 
tion of the sides of the vessel, or of any solid immersed in 
the fluid, will, in like manner, sustain a pressure in propor- 
tion to its area. 

139. A liquid is not at rest unless its molecules are 
somehow restrained by a vessel or its equivalent. In an 
open vessel, the force of gravity tends to bring each mole- 
cule as near the earth's center as possible. ^ J^ 
This will only be the case when the sur- 
face is perpendicular to the force of gravity ; 
for suppose the surface were curved, as in Fig. 69. 
Fig. 69, then a particle at M would exert a pressure by 
reason of its weight. This would be transmitted downward 
and sideways; but, as there would be no equal pressure be- 




WATER LEVEL. 93 

low A to counterbalance it, a part of its pressure would pro- 
duce motion in the fluid, and would finally bring the surface 
to the common level, AB. 

140. As two verticals, near each other, are sensibly 
parallel, any liquid surface between them is level or hori- 
zontal. As two verticals, drawn at distant points, incline 
toward each other, large surfaces of liquids are curved so as 
to correspond with the general form of the earth's surface.* 

141. Water always seeks its lowest level. It is on 
this principle that water is conveyed from reservoirs through 
pipes to supply cities. The water rises in the pipes to the 
exact level of the reservoir ; and would rise to the same 
level in fountains, were it not for the resistance of the air, 
and other impediments to motion. The spirit level, which 
is used to determine horizontal lines, operates on the same 
principle. 

This consists of a f* | ip . & B 

closed glass tube, 

Slightly Curved, and == ^m^mmmmm^^^^mm r 

& J Fig. 70. 

nearly filled with 

some liquid not easily frozen. The tube is then so placed 
in a brass case that when the apparatus is perfectly hori- 
zontal, the small bubble of air, J5, will lie exactly at the 
highest point. 

142. Fluids exert pressure in consequence of gravity. 
Suppose the vessels, AB CD, to be filled with any liquid to 
the same level, CD, and consider each divided into an infi- 
nite number of horizontal strata, as indicated by the lines 



*The amount of curvature increases with the square of the dis- 
tance, as shown by the following table: 

Distance in miles 1234 56 7 89 10 

Curvature in feet 667 2.67 6. 10.67 16.67 24. 32.67 42.67 54. 66.67. 



94 



ELEMENTS OF PHYSICS. 



A 



B 




of the diagram. Each stratum may then be considered as 
a cylinder exerting a pressure on its base equal to its own 
weight. By the law of 

fluid pressures, the weight q \ \j) c 

of each stratum above 
will be transmitted undi- 
minished to each stratum 
below in the ratio of their 
areas ; therefore, the press- 
ure sustained by any sec- 
tion, as AB, G L, G B, will be equal to the weight of a 
column of the liquid whose base equals the area of the 
section, and whose height equals its depth. 

143. The pressure exerted by a fluid is proportional 
to its depth. (1) The downward pressure of liquids may be 
illustrated by tying a piece of sheet rubber over one end of 
a long open tube. On pouring water into the tube the rub- 
ber will be distended in proportion to the depth of the 
water. (2) The upward pressure of liquids is easily shown 

by thrusting the closed end of the 
tube into water, when the rubber 
will be driven into the tube further 
and further as the depth increases. 
It is generally demonstrated by tak- 
ing an open tube, having disks of 
lead or leather closely fitting the lower 
end. Support the disk by a thread 
until the tube is plunged in a vessel 
of water. The disk will then be re- 
tained in its place by the upward 
pressure. If, now, the tube be care- 
fully filled, the disk will not fall off until the weight of the in- 
terior column plus that of the disk exceeds the weight of the 




Fig. 72. 



PASCAL'S EXPERIMENT. 



95 




exterior column. (3) The lateral pressure of liquids is shown 
by the velocity with which they flow from orifices at differ- 
ent depths. A fine illustration is represented in Fig. 73. 
It consists of a tall jar with a 
stop-cock near the base, and made 
to float on the surface of some 
liquid. If the jar be filled with 
water and the stop-cock closed, 
the lateral pressure at L and IJ 
will be equal. Hence, the jar 
will remain at rest, because the 
pressures are equal ; but on open- 
ing the cock, the Fig. 73. 
pressure at L is removed, and the lateral 
pressure at U will be effective in driving the 
float in the direction of the arrow, and op- 
posite to the course of the stream. 

144. The pressure is independent of the 
quantity of the liquid. In 1647, Pascal 
fitted to the upper head of a small cask 
a tube about forty feet long. The cask 
being filled with water, he succeeded in 
bursting it by filling the tube. As an ounce 
of water will fill a tube forty feet long and 
y 1 - of an inch in diameter, an ounce would 
have sufficed ; for a tube -^ of an inch in 
diameter has an area of only ^tt °f a square 
inch, so that the ounce weight would mul- 
tiply itself two hundred and seventy-seven 
times for each square inch on the vessel, 
Fig. 74. which becomes a pressure of 17.31 pounds 

for each square inch. Either head of an eight gallon cask 
would have to sustain a pressure of about two thousand 





96 ELEMENTS OF PHYSICS. 

five hundred pounds, and the total pressure on the cask 
would have exceeded fifteen thousand pounds. 

145. As fluid pressure is transmitted un- ^ 
diminished in all directions, it will not be af- 
fected by bends in the tube. The hydrostatic 
bellows consists of two boards, A B, united by 
stout leather, and a small tube, c, communi- 
cating with the interior. Water poured into 
the tube will lift the upper board, w r ith a force 
proportioned to the height of water in the 
tube. Each foot in height represents a press- 
ure of 0.4335 pounds to the square inch; 
therefore, if the upper board has an area of \ 
one hundred square inches, and the height of B 
the tube is three feet, the weight capable of FlG - 75 - 
being supported on A will be .4335 X 100 X 3 = 130.05 
pounds. 

146. If A had been made to rise toward an immovable 
bar placed above it, any substance between the board and 
the bar would have been compressed with the force of 43.35 
pounds for every foot in the height of the tube. By in- 
creasing the length of the tube, the pressure will soon be- 
come great enough to rupture the bellows. The same effect 
may be produced, if, instead of lengthening the tube, a piston 
is employed to force water down the tube. By the law of fluid 
pressures, a pressure equal to that upon the piston would be 
communicated to each equal area in the bellows. 

147. Bramah's hydraulic press is constructed on this 
principle. 

Within the collar of the iron cylinder, B, a cast-iron 
ram, P, works water-tight. The substance to be pressed is 
placed between the ram, P, and the immovable plate, Q. 
Water is brought by a force-pump into the small cylinder, 



THE HYDRAULIC PRESS. 



97 



A, and is thence driven by the piston, ?•, through the tube, 
K y into the larger cylinder. The advantage gained will be 
in proportion to the areas of the two cylinders. If the large 
cylinder is one hundred times the area of the small cylinder, 




Fig. 76. 

one pound applied at the piston will produce a pressure of 
one hundred pounds on the ram. The efficiency of the 
press is further increased by the handle, M, a lever of the 
second class. If the distance from the fulcrum to the applied 
force is ten times the distance to the weight, a power of one 
hundred pounds will transmit one thousand pounds to the 
piston, and tend to raise the ram by a force of one hundred 
thousand pounds. 

148. In this press very little power is lost by friction, 
and, practically, the advantage gained is limited only by 

Phys. 9. 



98 



ELEMENTS OF PHYSICS. 



the strength of the materials. Like all other machines, it 
is governed by the law of virtual velocities, and works very 
slowly. In the example supposed, one hundred parts of 
water driven out of the small cylinder would raise the ram 
but one part. The hydraulic press is used wherever great 
power is to be transmitted through small space, as in ex- 
tracting oils from seeds and crude fats, and in pressing 
cotton for shipment. Two of these machines were employed 
to raise the immense tubes of the Britannia Bridge to their 
proper elevation. Such was the force employed to drive 
the water into the cylinder, that it was sufficient to raise a 
jet twenty thousand feet high, or over the peak of Chimbo- 
razo. With such pressures, the weight of the water in the 
smaller cylinder becomes inconsiderable. 

149. The pressure is proportional to the density of the 
fluid. If mercury be poured into a U tube, so as just to 
fill the bend, and then water be poured into 
one arm of the tube, the mercury will be 
driven a little way into the other arm. Now, 
if we measure the height of the mercurial 
column above the lowest level of the water 
(represented in the figure by the dotted line), 
we shall find that it is y^§ as high as the col- 
umn of water. 

150. Principle of FlG - 77 
notation. Suppose a solid, A BCD, 
to be immersed in water, every por- 
tion of its surface will undergo press- 
ure. The horizontal pressures, on the 
sides of the body, will all be equal and 
opposite, and have no tendency to 
move the body in any direction. The 
upper face will be pressed downward by a liquid column, 





PRINCIPLE OF ARCHIMEDES. 



99 



MA B N, the lower face will be pressed upward by the 
liquid column, M CD N. The solid will, consequently, be 
urged upward by a pressure which equals the difference of 
these columns; MCDN—MABN=ABCD. This is 
equal to the weight of a volume of the fluid equal to the 
volume of the solid. 

Now, as the force of gravity tends to bring the body 
lower, and as the upward pressure of the fluid tends to 
raise it, the effect will be to lessen the apparent weight of 
the body. (1) A rare body, like cork, will rise to the sur- 
face, and finally displace a volume of the fluid equal to its 
own weight If attached to a balance it will exert no pull, 
and may be said to have lost all its weight. (2) A dense 
body will tend to sink deeper in the fluid, but if this is re- 
sisted by a string, the pull will be less than its whole weight 
by the w T eight of the volume of the fluid displaced ; that is, 
by the weight of a volume equal to its own bulk. 

151. This principle was discovered by Archimedes, about 
230, B. C. It may be verified by hanging to one arm of a 
balance a cup, A, and a solid cylinder, JS, 
which exactly fits within the cup. Having 
first counterpoised the balance by weights 
put in the other scale pan, immerse the solid, 
B, in water. The equilibrium will be de- 
stroyed, because the solid loses a portion of 
its weight, but will be restored when the cup, 
A, is filled with water. 

Therefore, a solid immersed in a fluid loses 
an amount of weight equal to the weight of an 
equal volume of the fluid. 

152. We can now understand how the 

specific gravity of solids is found (read pages 13 and 14). 




100 ELEMENTS OF PHYSICS. 

We first weigh the body in air, then suspend it by a hair 
and weigh it in water. The difference of the two weights is 
the weight of an equal volume of water. Hence, 

Weiqht of qiven substance in air & .„ 

•r * ryri 1 = upecvfic gravity. 

Loss of weight m water ± j j j 

Thus, a mass of lead, weighing a pound in air, weighs 
14.6 ounces in water. Its specific gravity is, therefore, 
16 -T- (16 — 14.6) = 11.4. 

153. When a solid is lighter than water, it is neces- 
sary to submerge it by attaching to it a heavy mass, whose 
weight in water and in air are known. The loss of the 
combined bodies is evidently the weight of water equal to 
their united volume. If the loss sustained by the heavy 
body alone is taken from this, the remainder will be the 
weight of water equal to the volume of the light body. 
The weight of the light body in air divided by this remain- 
der, will give its specific gravity. 

Thus, attach to a pound of lead two ounces of cork. The 
weight in water is 8.6 ounces. The loss of both bodies is 
16 + 2 — 8.6 = 9.4, but, as the the previous example shows, 
the lead loses 1.4 ounces, the weight of a volume of water 
equal to the cork is 9.4 — 1.4 = 8 ounces. Therefore, the 
specific gravity of the cork is 2 ~ 8 = .25. 

154. A floating body has a constant weight, but dis- 
places a greater volume of light than of heavy liquids. Hence, 
if these relative volumes may be found, the specific gravity 
of any liquid may be found by dividing the volume which 
a floating body displaces in water, by the volume which it 
displaces in a given liquid. This is the principle of the 
hydrometer. 

The hydrometer consists of a glass stem, near the bottom 
of which are blown two small bulbs. Some mercury or shot 



THE HYDROMETER. 



101 






is placed in the lower bulb, to serve as ballast, and the 
point to which the instrument sinks in pure water is marked 
on the stem. It is then placed in a liquid whose specific 
gravity is known; the point to which it sinks is marked, 
and the intermediate space sub- 
divided into equal spaces, called 
degrees. The value of these de- 
grees in terms of specific gravity 
is then determined by a mathe- 
matical calculation. These in- 
struments do not give accurate 
results, but are of convenience 
for rapid determinations. 

A farmer roughly esti- 
W mates the density of brine 

by noticing whether an 

egg or a sound potato 

will float in it. 

The specific gravity of liquids is accurately found 

by the specific gravity bottle, Fig. 81, by means of 

which we are enabled to weigh equal volumes of 

two liquids. 

The weight of any given liquid ~ •* •. 

81# The weight of an equal volume of ivater r J y J- 

155. The speoific gravity of gases is found in the same 
way, only it is necessary to use very large flasks. 




Fig. 80. 



Recapitulation. 



I. Liquids are both compressible and elastic. 

IT. They produce pressure by their weight, proportional to their 
depth, and transmit it as if it were an external pressure. 

III. They transmit external pressure in every direction, 



» 

102 ELEMENTS OF PHYSICS. 

■ 

1. Undiminished. 

2. Perpendicular to their surfaces. 

3. Proportional to their areas. 

IV. A liquid always seeks its lowest level. 

V. The surface of a liquid at rest is horizontal. 

VI. The upward pressure of a liquid upon a solid is equal to the 
weight of the fluid displaced. 

1. A submerged solid loses weight equal to the weight of the 

fluid of the same volume. 

2. A floating solid loses all its weight, and displaces a volume 

of the fluid equal to this weight. 

VII. The standards for specific gravity are water for solids and 
liquids ; and air for gases. The normal conditions are a temperature 
of 39. °1 F. for water and 32° F. for all other bodies, and a barop 
pressure of 29.922 inches. 

VIII. The specific gravity of a body is found by comparis3 
water and air. 

1. By the relative weights of equal volumes. 

2. By the relative volumes of equal weights. 

V 

Problems. 

1. A reservoir is 120 feet long, 40 feet wide, and 20 feet deep; 
what is the weight of the water contained in it? What is the pres- 
sure on the bottom? On each side? The total pressure? 

2. A mass of galena weighs 6 ounces in air and 4.8 ounces in 
water ; what is its specific gravity ? Q 

3. The same mass attached to an ounce of cork weighs in water 
2.7 ounces; what is the specific gravity of the cork? 

4. A flask contains 900 grains of water, 800 grains of alcohol, or 

1,350 grains of sulphuric acid ; what is the specific gravity of the 

alcohol? Of the acid? 

J / <J 

5. A boy's marble weighs in air 450 grains, in water 300 grains, in 
coal-oil 350 grains; required, the specific gravity of the marble and 
of the coal-oil. 5 51^ 

6. If the upper board of the hydrostatic bellows has an area of 100 
square inches, and a boy standing upon it raises water in the pipe 
to the height of 30 inches, what is the weight of the boy? 




3 $6' 



CHAPTER X. 

FLUIDS IN MOTION. 



156. We learned, in the preceding chapter, that the press- 
ure of a fluid is proportional to its depth. Hence, if a 




Fig. 82. 
vessel be filled with a liquid, and apertures r, q, m, n, p, 
be opened, the liquid will flow out with unequal velocities, 
being less for r than for any point beneath it, and equal for 
any two points at equal depth below the surface, as p and v. 
But the velocity does not increase in the simple ratio of the 
depth. The jet at v tends to rise to the level at h, and 
falls short of it only because of friction, the resistance of 
the air, and the weight of the particles falling back. If, 
then, the velocity at v is sufficient to carry the liquid 
through the vertical distance, vh, in opposition to gravity. 
this velocity must be equal to that ivhich a body would acquire in 
falling through the same space; and this must be true for any 

(103) 



104 ELEMENTS OF PHYSICS. 

aperture. Hence (by page 60), the velocity with which 
a liquid escapes from an orifice increases with the square 
root of the depth below the surface. 

157. The course of a stream spouting out in any other 
direction than the vertical, is that of a parabola. We can 
easily calculate the range of a horizontal jet. For example : 
if the jet, q, is four feet below the surface, the velocity due 
to the depth, hq, is sixteen feet per second. If its height 
above ab, the level on which it strikes, is nine feet, it will 
be three-fourths of a second in falling. As these two mo- 
tions do not interfere with each other, the range wdll be 
found by multiplying the velocity by the time (16 X f = 12). 
The range of a jet will be the greatest when it is midwa^ be- 
tween the surface and the level at which it strikes. Any 
orifice, as n, as far below the middle point as q is above it, 
will have an equal range with q, for although its velocity is 
greater, it has a less time to fall, and the products are the 
same in both cases. (The resistance of the air being re- 
moved.) 

158. The now of water in pipes is much retarded by 
friction and other causes, and, unless a large allowance is 
made for these, the quantity delivered will fall short of the 
estimate. Under ordinary circumstances, the diameter of 
the discharge pipe should be one-half greater than that re- 
quired by theory. 

159. Running water acts as a motive pow T er (1) by its 
weight, (2) by the force of the current, or (3) by the com- 
bined effect of both. Water-wheels are either vertical or 
horizontal. In vertical wheel, the effective power of the 
stream is applied to buckets or boards fixed on the circum- 
ference. The wheel is connected with the machinery to be 
moved. There are three varieties of vertical w T heels: (1) 
the overshot, (2) the undershot, and (3) the breast-wheel, 



WATER-WHEELS. 



105 



which receive their names according as the water strikes 

near the top of the wheel, as 
in Fig. 83; or at the bottom, 
as in Fig. 84; or somewhere 
near the axis, as in Fig. 85. 




Fig. 83. Fig. 84. 

160. The availability of any wheel depends on the 
character of the fall. Undershot wheels are adapted to low 




;xf00&/wy////s 



Fig. 85. 



falls or rapids with large supplies of water. Overshot 
wheels are used with falls not exceeding sixty feet in height, 
and are efficient even with small streams. Breast-wheels 
require a larger supply of w T ater, but the fall is always less 
than their diameter. 

161. There are two forms of horizontal wheels ; (1) the 
reaction, (2) the turbine. 



106 



ELEMENTS OF PHYSICS. 




The reaction wheel acts on the principle of unbalanced 
lateral pressure (page 95). 

A vertical axis, CD, which re- 
volves upon a pivot, terminates in 
in two horizontal pipes, A and B, 
whose extremities are curved in op- 
posite directions. As the fluid es- 
capes from the orifice in the ends of 
these pipes, the arms are driven 
around in opposite directions to 
the flow, and may be employed to 
communicate motion to machinery. 

162. There are three classes of turbines, and many 
varieties of each class. One of the most efficient was in- 
vented in 1827, by M. Fourneyron. Fig. 87 shows a verti- 
cal, and Fig. 88, a horizontal section of this turbine. . 

A column of water, con- 
fined in a cylinder, B, 
after descending in its 
vertical axis, rushes out 
at the bottom, through a 
great number of guides, 
so as to strike the 



Fig. 86. 





Fig. 87. Fig. 

curved buckets, 6, of the wheel, and make it revolve. The 
buckets are so curved as (1) to receive the impulse of 
the water in the direction of its greatest efficiency ; and then 



TURBINES. 107 

(2) to permit its escape with the least loss of motion. The 
wheel is connected beneath the cylinder to the shaft, d, 
which passes upward through the center of the cylinder, 
and communicates its motion to the gearing at the upper 
end of the shaft. Turbines are applicable to falls of any 
height, from nine inches upw T ard, and will utilize from .75 
to .90 of the power of the water. 

Recapitulation. 

I. The velocity of a liquid jet is that which a body would acquire 
in falling through a space equal to its depth below the surface. 

II. Running water exerts a power in proportion to its weight and 
the square of its velocity, diminished by the impediments to mo- 
tion. 

III. It acts as a motive power in water-wheels: 

Useful 
Effect. 

("Undershot 25 

1. Vertical i Breast .60 

I Overshot 75 

n TT . . , /Reaction 40 

2. Horizontal 1 

L Turbine 80 

Problems. i \ 

1. A reservoir of water is 64 feet high; with what velocity wilL; 

water flow from an orifice 16 feet below the surface? 25 feet? \3§y L "i^ y 
feet? 64 feet? What are the ratios between these velocities? Wha^y ^jr 
will be the range of a stream escaping from an orifice at the center ±1 / 
of the reservoir? J (J l l J I _ • 

2. Suppose a pipe an inch in area was attached to each of these 
orifices, what would be the theoretical discharge of water per min- 
ute? 

3. The source of the Mississippi is 1,572 feet above its mouth ; if 
its flow were entirely unimpeded, what would be its final velocity? 



CHAPTER XI. 

THE PHENOMENA OF AERIFORM FLUIDS. 

163. The atmosphere is mainly a mixture of two gases, 
oxygen and nitrogen. These constituents have never been 
obtained in a solid or a liquid state. Most gases have been 
condensed into liquids by the aid of pressure and of low 
temperature, and some so easily that they are frequently 
considered as a separate class under the name of vapors. 
Steam is the type of all vapors. Nevertheless, there is no 
difference between a vapor and a gas, except such as results 
from their specific properties, as density, odor, etc. Hence, 
whatever physical property may be established regarding 
atmospheric air, will be understood as applying to all 
bodies, so long as they are in the aeriform state. 

164. Air has been proved to possess extension, impen- 
etrability, compressibility, mobility, and inertia, which are 
essential properties of matter. Like all other fluids, it 
transmits pressure undiminished in every direction; but, as 
its compressibility far exceeds liquids like water, the effect 
of pressure is not felt as instantaneously at long distances as 
in the case of liquids. 

165. The air is kept in its place about the earth by the 
joint action of the attraction of gravitation and the repul- 
sive force which exists between its molecules. Consequently, 
the atmosphere, at its upper limit, must have a definite sur- 
face like the sea. At any point on the earth's surface, the 
air will exert, by reason of gravity, a pressure due to a line 
of molecules extending from that point to the upper limit 
of the atmosphere. 

(108) 



PRESSURE OF THE ATMOSPHERE. 



109 



166. The pressure of the atmosphere may be illus- 
trated by many simple experiments. 




Fig. 89. 





Fig. 91. 



(1) In the pneu- 
matic inkstand, Fig. 
89, the downward 
pressure of the at- 
mosphere on the 
liquid in the tube Fig. 90. 
sustains the ink in the bottle. When the 
ink sinks down to the level of the neck, 
a bubble of air passes in and forces out a 
portion of the ink into the tube. 

(2) Fill a tumbler with water, and, 
having placed a thick slip of paper over 
its mouth, press the paper down tightly 
with the hand, and invert the glass cautiously. The hand 
may now be removed, and the water will be supported in 
the glass by the upward pressure of the atmosphere on the 
paper, Fig. 90. 

(3) Take a small open tube, or a pipette, Fig. 91, plunge 
it vertically in water until it is filled, then close the upper 
end with the finger and raise the tube. The water will not 
run out because the pressure of the air keeps it up. Re- 
move the finger, so that the atmosphere may press above 
and below, and the water will fall by its own w T eight. 

(4) Water will not flow out of a small tap in a tight 
barrel, because of the lateral pressure of the atmosphere. If 
this be counteracted by admitting air through an opening 
in the top, the water will run freely by its own weight. 




110 ELEMENTS OF PHYSICS. 

No upper opening is required in beer barrels, because of the 
tension of the gases contained in the beer. 

(5) A boy's sucker is made by attaching a stout string to 
the center of a small circular piece of thick leather. The 
leather is first soaked in water, and then pressed firmly 
against the smooth surface of a stone, so as to exclude all 
the air. The two surfaces are now held to- (( i;a/^ 
gether by the force of fifteen pounds to the F 

square inch, Fig. 92. On pulling the string, 
a vacuum is formed under a portion of the 
leather, and the weight of the atmosphere on 
its upper side is borne by the hand. The 
weight of the atmosphere is thereby removed 
from this portion of the stone, and, if it is 
not too heavy, the pressure of the atmosphere fig. 92. 
on its under side will raise it up. 

167. The barometer, described on page 20, is used for 
measuring atmospheric pressure. At the level of the sea, 
the mercurial column varies in height from twenty-eight to 
thirty-one inches, the average being, for London, 29.922 
inches. This pressure will sustain a column of water 33.9 
feet high. 

168. Mercury is about eleven thousand times denser 

than the air at the level of the sea. If the air were every- 
where of this density, the height of the atmosphere required 
to balance the barometric column would be 11000 X 29.922 
inches, or twenty-seven thousand four hundred feet. The 
pressure of the air may, therefore, be reckoned as equal to 
a column 5.2 miles high, having throughout a density equal 
to that of air at the sea level. 

We know that aeronauts have ascended seven miles. We 
know also that the air must become rarer as we ascend from 
the level of the sea, because the air at any level is com- 



PRESSURE OF THE ATMOSPHERE. 



Ill 



pressed by the weight of the column above it. If a barom- 
eter were carried one thousand feet above the sea level, the 
column would descend about an inch. At the height of fifty 
miles, the mercurial column would be elevated about one- 
thousandth of an inch. This height, therefore, may be con- 
sidered as the practical limit of the atmosphere. 

x A TNCHEF 

Fig. 93 is an attempt to represent to the eye 
the decreasing pressure of the atmosphere. 

169. Heights are measured by the barom- 
eter, in accordance with the observed rate of the 
decrease in atmospheric pressure. Observations 
are taken at two stations at very nearly the same 
moment. The difference between the two 
barometric columns will represent the differ- 
ence in the atmospheric columns above the 
two stations, from which the vertical distance 
between the stations mav be calculated. 




Fig. 93. 



170. The atmosphere may be regarded as 

an aerial ocean, in whose lower depths we live. 
From the extreme mobility of its particles, it 
is never perfectly at rest, but moves in im- 
mense waves above our heads. When the 
crest of one of these waves is over the barome- 
ter, the column rises, and then again falls as the hollow 
of the wave succeeds. This will give rise to variations 
which are dependent on the season and even the hour of 
the day, but which succeed each other in periods which are 
very nearly regular. 

171. The barometer is subject also to irregular varia- 
tions, which are often coincident with the changes in the 
weather. The absolute height of the column varies with 
the altitude of the station, and affords, by itself, no indica- 
tion of the weather; hence, the weather marks, "fair, rain, 



112 



ELEMENTS OF PHYSICS. 



wind," on some barometers, are worthless. The barometer 
measures only the pressure of the atmosphere, and vari- 
ations in its height indicate variations in this pressure, 
which, if they occur at irregular intervals, may be followed 
by changes in the weather. 

Rules for predicting changes in the weather : 

(1) The rising of the mercury indicates the approach of 
fair weather ; the falling of the mercury indicates the ap- 
proach of foul weather. 

(2) A sudden and great fall indicates a violent storm. 

(3) When the barometer changes slowly, 
a long continuance of the weather indicated 
may be expected. 

(4) A sudden change of the barometer indi- 
cates that the change of weather will not be 
of long duration. 

172. Thus far we have considered the 

air in the free state ; let us see how it acts 

when confined. Bend the closed end of a 

barometer tube, as in Fig. 94, and pour in 

just enough mercury to fill the bend. The 

inclosed air is in its natural state, under the 

pressure of one atmosphere. If thirty inches 

of mercury be poured in the open arm, the 

confined air will be under the pressure of two 

atmospheres, one of mercury and the other of 

air, and will be reduced in volume one-half. 

If thirty inches more mercury be added, the 

pressure will be three atmospheres, and the 

volume will be reduced to one-third, and so on. fig. 94. 

Therefore: (1) The volume of a given weight of air decreases as 

the pressure to which it is exposed increases. 



MARIOTTE'S LAW. 



113 



This statement is known as Mariotte's law, and is true for 
all gases within small limits of error. Now, as the volume 
decreases its density increases ; therefore, 

(2) The density of a given weight of air is directly as the press- 
ure to which it is subjected. 

Finally, as the pressure is always sustained by the elastic 
force, or tension, of the inclosed air, 

(3) The tension of a given weight of air is directly as Hie 
pressure to which it is subjected. 

Consequently, 

(4) The density and tension of a given weight of air ivill 
increase as its volume is decreased, and will decrease as its volume 
increases. 

173. Mariotte's law applies both to con- 
densed and to rarified air. The proof for 
pressures less than one atmosphere may be 
made by filling a barometer tube to within four 
inches of the top with mercury, and then in- 
verting it in a tall cistern of mercury, Fig. 
95. When the tube is sunk until the level 
of the mercury is the same as in the cistern, 
the confined air will be under the pressure of 
one atmosphere. When the tube is raised, the 
pressure exerted on the air will be one atmos- 
phere minus the weight of the mercury raised 
in the tube. If the column is raised fifteen 
inches, the air will have doubled its volume, 
and will have decreased one-half both in 
densitv and in tension. FlG - 95 « 




174. The tension of aeriform fluids is measured by 
manometers or gauges. One of the simplest forms is the 

Phys. 10. 



114 



ELEMENTS OF PHYSICS. 



closed manometer, Fig. 96. It consists of a U tube, closed 

at one end, and half filled with mercury. The closed end 

contains dry air. When the open end 

communicates freely with the atmosphere, 

the level of the mercury is the same in 

both parts of the tube, showing that the 

inclosed air is under a tension due to one 

atmosphere. 

Now, if the open end is connected with 
vessels containing aeriform fluids whose 
tension is to be measured, as with steam 
in a boiler, the confined air will be reduced in volume to 
one-half, one-third, etc., according as the pressure increases 
to two, three, etc., atmospheres. Or, if the pressure is less 
than one atmosphere, the inclosed air will expand as the 
pressure decreases. ^ 




Fig. 96. 



AlR-PuMPS. 



175. An air-pump is an instrument for removing the air 
from a closed vessel. 

Fig. 97 shows the Leslie air-pump, and Fig. 98 the same 
instrument in section. The receiver, R, is connected with 
the cylinder, C, by a long bent tube, terminating in a hori- 
zontal brass plate. The mouth of the receiver and the sur- 
face of the brass plate are carefully ground, so as to bring 
them in contact at every point. The edge of the receiver 
is smeared with grease, so as to render the connection as 
close as possible. 

When the piston, P, is raised from the bottom of the 
cylinder, the external air closes the upper valve; the air in 
the receiver expands, opens the lower valve, and fills the 
cylinder. When the piston is depressed, the lower valve 
closes, and the air in the cylinder is forced through the 



THE AIR-PUMP. 



115 



upper valve out into the atmosphere. As the piston again 
rises the upper valve is closed, the lower valve opens, 




Fig. 97. 



At every 




and the confined air expands into the cylinder, 
ascent and descent of the piston, 
a portion of air is removed from 
the receiver ; and this process may 
be repeated until the tension of 
the air remaining is not sufficient 
to lift the lower valve. The re- 
ceiver is then said to be exhausted. 
The tension of the air in - the 
receiver is measured by a gauge, 
which consists of a bent tube, 
leading from the receiver to a ves- 
sel of mercury, H. The external air forces the mercury up 
the gauge, in proportion as the tension of the air in the 



#4^ 



is A 
4= 




Fig. 98. 



116 



ELEMENTS OF PHYSICS. 



tube is diminished. If the exhaustion were perfect, the 
mercury would rise to about thirty inches. The height of 
the gauge indicates the difference between the pressure of 
the atmosphere and the tension of the air in the receiver. 

The air-pump is also provided with a stop-cock, S, to 
close the communication between the cylinder and receiver 
when required. The stopper, A, is used to admit the ex- 
ternal air to the receiver. A third valve, t, is usually 
placed in the top of the cylinder to prevent the external 
air from pressing on the piston. 

176. The air-pump may be used to perform a great va- 
riety of experiments, illustrating the properties of the air, 
only a few of which can here be given. 

(1) The presence of air in bodies may be shown by placing 
a jar of well-water under the receiver. On working the 
pump, bubbles of air will be disengaged from the water. 
Having freed the water from air, fasten to the bottom of 
the jar bits of wood or other solids, and repeat the experi- 
ment. The formation of air bubbles will prove their poros- 
ity, and the presence of air in the pores. 

(2) Expansibility. Tie the neck of a fresh, flaccid bladder 
and place it in the receiver. On exhausting the receiver, 
the bladder will dilate, because the air 
within it expands. On re-admitting 
air to the receiver, the air in the 
bladder resumes its former volume. 

A withered apple, or a bunch of 
shriveled grapes will become plump in 
an exhausted receiver. 

(3) Pressure of the atmosphere. Take 
a small open receiver, close the upper fig. 99. 
end tightly with a piece of moistened bladder, and suffer the 




THE MAGDEBURG HEMISPHERES. 



117 



bladder to dry. On exhaustion, the external pressure will 
generally be sufficient to burst the bladder with a loud 
report. If the bladder is very stout, or the exhaustion in- 
complete, it may be necessary to weaken the strength of 
the membrane by puncturing it with the point of a pin. 

Tlie Magdeburg hemispheres, Fig. 100, consist of two hollow 

brass hemispheres, which fit together air- 
tight. One of them may be connected 

with the air-pump by a tube and stop-cock 

arrangement. On exhausting the air from 

the interior, the two hemispheres will be 

held together with a force of fifteen pounds 

to the square inch. If their diameter is 

three inches, the area of the section will 

be seven inches, and the force which holds 

them together will be over one hundred 

pounds. As the restraining force is the 

same in every position in which they are fig.ioo. 

held, the pressure of the atmos- 
phere is Hie same in every direction. 
Fig. 101 represents a tall re- 
ceiver, which terminates in a 
metallic cap, furnished with a 
stop-cock, a screw, and an in- 
terior jet pipe. Exhaust the 
air from the interior and close 
the stop-cock. Place the mouth 
of the tube under water and 
open the stop-cock. The press- 
ure of the atmosphere will drive 
the water up the pipe, form- 
ing what is known as the 
F IG . ioi. vacuum fount ah i. 





118 



ELEMENTS OF PHYSICS. 




Fig. 102. 



The weight lifter consists of a receiver, which is connected 
to the air-pump by an opening in the top. The lower end 
is closed by a piston or by a stout rubber bag. When the 
air is withdrawn from the receiver, the bag 
is forced upward, and carries with it weights 
attached below. If the receiver is five 
inches in diameter, nearly three hundred 
pounds will be lifted by the upward pressure 
of the atmosphere, if the vacuum is complete. 

(4) When a heavy weight is thus sus- 
tained, the elasticity of the air may be shown, 
in a striking manner, by forcing down the load by the hand, 
and then releasing it. The weight will then oscillate up 
and down, as if on an elastic spring. 

(5) The weight of air may be ascertained, by taking a 
vessel of known capacity and finding the difference of its 
weight when filled with dry air, and when exhausted of air. 
If the capacity of the vessel is one hundred cubic inches, 
the difference of its weight will be thirty-one grains. There- 
fore, the weight of one cubic inch of air is 0.31 grains. 

(6) The buoyancy of air. 
By the principle of Archim- 
edes, a solid immersed in 
a fluid loses an amount of 
weight equal to the weight 
of an equal volume of the 
fluid. Hence, every sub- 
■ stance weighs less in air than 
in vacuo. 

Suspend to one arm of a 
balance a hollow globe, or a 
Fig. 103. ball of cork, and counter- 

poise it with a lead weight. Now place the balance under 




THE BALLOON. 119 

a receiver and exhaust the air. The globe or the cork 
will fall, and thus seem to be heavier than the lead. 

If a body is lighter than an equal volume of air, it will 
rise in it. Smoke rises in a chimney because air is rarified 
by heat. A soap-bubble, filled with warm air, rises because 
it weighs less than the air it displaces. If the soap-bubble 
is filled with hydrogen, it rises rapidly until it bursts. 

Balloons are varnished silk bags, filled with hydrogen. 
The buoyant effort of the air in raising a balloon is equal to 
the difference between the weight of the gas used and the 
air displaced by it. A spherical balloon, forty feet in diam- 
eter, will displace two thousand five hundred pounds of air, 
but will contain less than two hundred pounds of hydrogen. 
The lifting force of such a quantity of gas is over a ton. 
It is, therefore, jcapable of lifting the weight of the balloon, 
the aeronaut, and a large quantity of sand used for ballast. 
If the aeronaut wishes to descend from a height, he allows 
some of the gas to escape, by opening a valve in the balloon. 
If he wishes to rise again, he throws out a portion of his 
ballast. 

(7) That air is necessary to combustion, may be shown by 
placing a lighted candle in a receiver. On working the 
pump, the candle will grow dimmer, burn blue, and finally 
go out. The smoke of the candle will be seen to descend 
because there is nothing to sustain it. 

(8) That air is necessary to animal life, may be shown by 
placing a bird or a mouse in a receiver. On exhausting the 
air, the animal will give evident signs of distress, and will 
soon die. 

(9) The relations of air to sound and heat will be consid- 
ered hereafter. 

177. The body of a man of average size has a surface 



120 ELEMENTS OF PHYSICS. 

of about two thousand square inches. He, therefore, sus- 
tains, at the level of the sea, a pressure of thirty thousand 
pounds. It conveys a wrong notion to speak of this press- 
ure as a load ; on the contrary, the buoyant effort of the 
air lifts the man, and makes him press the ground more 
lightly than he would without it. The atmosphere acts on 
all sides of a body immersed in it, not as a weight, but as 
a crushing force. The reason why we do not feel this com- 
pressing force is because the pressure is transmitted 
throughout the body by the blood and other fluids of the 
body. Hence, when the atmosphere tends to squeeze in 
the sides of the blood-vessels, it is met by an equal out- 
ward pressure, caused by the pressure of the atmosphere on 
the other parts of the system. 

We may become sensible of this outward pressure by 
placing the hand on a small open receiver and exhausting 
the air from beneath it. The external air now acts as a 
load, holding the hand firmly to the receiver. The blood, 
in the under surface of the hand, distends the vessels, 
and, if the skin has been punctured with a pin, the blood is 
forced out. Cupping-glasses are made to act on the same 
principle. 

178. The condenser is an instrument for forcing a large 
amount of air into a closed vessel. 

One of the best forms is shown in Fig. 104. It consists 
of a cylinder, C, in which a solid piston works air-tight. 
There are two valves in the cylinder, (1) the lateral valve, 
a, which opens from the outside, and (2) the low T er valve, b, 
which opens from the inside. The receiver, R, may be con- 
nected by a screw to the cylinder, and may be opened or 
closed by means of stop-cocks arranged as in the figure. 

In using this instrument, the condenser and receiver are 
connected and the piston driven down. This action con- 



THE AIR-GUN. 



121 



denses the air in the cylinder enough to close the lateral 
valve and open the lower. When the piston has reached 
its lowest point, all the air 
will be forced out of the 
cylinder into the receiver. 
The confined air will have 
its volume diminished and 
its tension increased. If 
the cylinder and receiver 
are of the same size, the 
condensed air will have a 
tension of two atmospheres. 
On raising the piston, the 
tension of the air in the re- 
ceiver will close the lower 
valve, the external atmos- 
phere will open the lateral 
valve, and again fill the 
cylinder. 

This operation may be re- 
"peated until the receiver is 
filled with air of the tension 
desired. When the receiver fig. 104. 

is thus charged, the stop-cock, V, is closed, and the cylinder 
is detached. 

By bringing the lateral valve in communication with a 
reservoir containing any gas whatever, this gas will be with- 
drawn from the reservoir and forced into the receiver. In 
this manner liquids placed in the receiver may be charged 
with gases. 

179. An air-gun consists of a charged receiver, properly 

connected to a gun -barrel. After fitting a bullet to the 

bottom of the barrel, a trigger turns the stop-cock, and the 
Phys. 




122 



ELEMENTS OF PHYSICS. 




condensed air rushes out with great force. A boy's pop-gun 
also illustrates the tension of confined air. 

A fountain can be arranged to play 
by condensed air. Before charging 
the* receiver fill it partially with wa- 
ter, and connect to the stop-cock a 
tube reaching to the bottom of the 
receiver. When the air has been con- 
densed and the stop-cock is opened, 
the air will force the water in a jet 
to a height proportional to the tension. 

The experiment may be varied by fig. 105. 

making the stream turn a horizontal tube, arranged on the 
principle of the reaction wheel, Fig. 105. 

180. If we place one end of an open tube in water, 
and apply the mouth to the other end, we may cause the 
liquid to rise in the tube by suction. Correctly speaking, 
the effect of the suction is to diminish the pressure in the 
tube; the water is then forced up the tube by the pressure 
of the atmosphere on the surface of the water in the vessel. 

The common suction, or lifting-pump, acts on the same 
principle. It consists of a barrel, B, similar to the cylinder 
of the air-pump, and, like it, fitted with a piston, P, work- 
ing air-tight, and two valves, U and e, both opening upward. 
From the bottom of the barrel proceeds the suction-pipe, C. 
which dips below the surface of the water to be raised. 

When the piston is worked, the air beneath it is rarefied 
more and more at each stroke ; the pressure of the atmos- 
phere causes the water to rise in the pipe and enter the cyl- 
inder through the lower valve. Now, on forcing down the 
piston, the lower valve, e, is closed, the water forces open 
the piston -valve, U, and rises above it. When the piston 
is again raised, the upper valve, U, is closed, and the water 



. 



THE SUCTION -PUMP. 



123 



bove it is lifted to the spout of the pump. At the same time, 

the atmospheric pressure on the water in the reservoir, causes 

more water to rise into the bar- 

• rel under the piston. 

181. The length of the suc- 
tion-pipe can never exceed 
thirty -four feet, because the 
pressure of the atmosphere is 
capable of supporting a column 
of water only thirty-four feet 
high. Owing to variations in 
atmospheric pressure, and the 
imperfect mechanism of the 
pump, the limit, in practice, is 
less than twenty-eight feet. There 
is, however, no limit to the height 
through which water may be 
lifted after it has once passed 
above the piston. In deep wells, 
the working -barrel, containing 
the piston and both valves, is 
placed near the bottom. A long, 
vertical discharge -pipe, through 
which the piston-rod plays, con- 
nects the working -barrel to the 
surface of the ground. The at- FlG ^ 
mospheric pressure forces the water from the well into the 
working -barrel ; the force applied to the piston lifts the 
water from the working-barrel to the top of the discharge- 
pipe. 

182. In the foreing-pump, the piston is made solid, and 
the upper valve, u, is placed in a lateral discharge-pipe, rf, 
connected with the bottom of the barrel. 




124 



ELEMENTS OF PHYSICS. 




Fig. 107. 



The lower valve and suction-pipe are the same as in the 
lifting-pump. When the piston is raised, the water passes 
up the suction-pipe through the lower valve, e, into the 
pump -barrel. On depressing the piston, 
the lower valve closes, and the water is 
forced through the upper valve, u, into the 
discharge-pipe. On again raising the pis- 
ton, the upper valve closes, and prevents 
the water in the discharge-pipe from re- 
turning ; the lower valve opens to admit 
more water into the barrel. At each de- 
pression of the piston, more water is driven 
into the discharge-pipe, until it is elevated 
to the required height. 

183. The water will be ejected from such a pump in 
successive impulses. When it is desired to make the stream 
continuous, an air-chamber is attached, as in Fig. 108. When 
the piston descends, it forces the water through the valve, u, 
into the air-chamber, A ; the water partially fills the chamber, 
and thus compresses the air. The tension 
of the compressed air increases as its bulk 
is diminished, and soon becomes sufficient 
to force the water in the chamber out 
through the tube, T, in a constant stream. 

184. An ordinary fire-engine consists 
of two force-pumps, worked by long 
handles, called brakes, and having an air- 
chamber common to both. The piston 
of one barrel descends as the other as- 
cends, by which means a continuous 
stream of water is forced into the air- 
ohamber, and escapes through the discharging-pipa 

185. The siphon is employed for transferring liquids 




Fig. 108. 



THE SIPHON FOUNT A IX. 



125 




from a higher to a lower level. It consists of a bent tube 
with two unequal arms, Fig. 109. In using the siphon, the 
shorter arm is plunged in the liquid to be transferred. To 
begin the action, the air may be removed from d m 
the tube by suction at the lower end. The liquid 
will be forced up the shorter arm by the pressure 
of the atmosphere ; it will then fill the tube and 
continue to flow through the siphon. 

After the suction is stopped, the liquid is 
pressed up in the shorter arm by the weight 
of the atmosphere on the surface, A B, minus the weight of 
the liquid column, ML So, also, the liquid in the longer 
arm is pressed upward by the weight of the atmosphere, 
minus the weight of the liquid column, M K. Hence, the 

liquid is urged in the direction, 
CMF, by a force equal to the 
excess of the weight of MK 
over that of ML If MK and 
ML were equal, there could be 
no flow in either direction. The 
greater the difference in the 
length of the arms, the greater 
will be the velocity of the flow. 
186. These facts may be pret- 
tily shown by the siphon foun- 
tain. Close the mouth of a tall 
flask, R, with a cork, and insert 
two glass tubes, as shown in Fig. 
110. The shorter arm should be 
drawn out at the upper end to a 
very fine bore. On exhausting 
FlG no - the air from the tube, the ordi- 

nary flow of the siphon will commence. If, now, the longer 




126 



ELEMENTS OF PHYSICS. 



may 



arm be lengthened, by attaching a rubber tube, the jet 
be made to strike forcibly against the top of the flask. The 
force of the jet may be shown to be dependent on the differ- 
ence in the length of the two arms. 



Friction of Fluids against each other. 




187. The atomizing tube is a contrivance for breaking 
up the particles of a liquid 
into spray. A common form 
is shown in Fig. 111. It 
consists of two open tubes, 
so inclined to each other 
that a jet of fluid driven 
through one shall issue over 
or near the mouth of the fig. hi. 

other. The blast tube, A y is usually contracted at its mouth, 
so as to increase the velocity of the stream. The lower end 
of the suction tube, J5, is plunged in any liquid, as cologne. 

If a stream of air is driven forcibly through the blast tube, 
it will, on issuing from the mouth, drag the contiguous par- 
ticles of air along with it, and thus produce a rarefaction 
behind it. As the air is rarefied in the suction tube, B, the 
atmospheric pressure on the liquid will force a column up- 
ward in the tube, and, if the tube be not too long, the par- 
ticles will rise to the top. At this point, the jet of air will 
drag the liquid molecules along with it, and the two streams 
will be mingled in one of excessively fine spray. 

The same principle is sometimes employed in producing a 
draft in chimneys and locomotives. In locomotives the waste 
steam is driven through a blast pipe in the smoke stack, and 
carries the smoke along with it, and thus increases the draft 
of the fire. 




THE PNEUMATIC PARADOX, 127 

188. The pneumatic paradox affords another illustration 
of the same sort. It may be made by taking two small 
disks of card board, and fitting to one a small tube. Now, 
if the other disk is placed above the 
tube, and a pin passed through the 
center to keep it from sliding, it can 
not be blown off by any ordinary cur- 
rent of air driven through the tube. 
Because, as the air is driven between fig. 112. 

the disks, a rarefaction will be produced at the center of the 
upper disk ; the air above it will crowd it toward the orifice 
and hold it the more firmly as the blast is made stronger. 
While the current of air is passing, the tube may be held 
in any position. The force requisite to blow away the upper 
disk must exceed the atmospheric pressure holding it down. 

Recapitulation. 

1. Aeriform fluids are governed by the same laws as liquids, except 
that, by reason of their compressibility, their volume is inversely, 
their density and tension directly, as the pressure to which they are 
subjected. 

2. All gases, like air, may be shown to possess the universal proper- 
ties of matter; but, except air, none are necessary to the support of 
animal life, and few are concerned in ordinary combustion. 

3. The barometer measures the pressure of the atmosphere, and may 
be used : 

(1.) To calculate the altitude of a place. 
(2.) To predict changes in the weather. 

4. The pressure of the atmosphere is employed in pumps and 
siphons. 

5. The friction of fluids against each other is employed in blast- 
pipes. 



CHAPTEE XII. 

THE MODES OF MOLECULAR MOTION. 

189. The topics considered in the last eight chapters natu- 
rally fall into two groups. (1) Phenomena which relate to 
bodies in equilibrium ; these belong to the science of statics. 
(2) Phenomena which relate to bodies in motion ; these be- 
long to the science of dynamics. Statics and dynamics taken 
together constitute the science of mechanics, which treats of 
bodies in equilibrium and in motion. 

Now, it will be noticed that in these chapters we have 
studied the effect which force produces upon a body taken 
as a whole. It is true that the force of gravity acts- upon 
every molecule of a body, but we have always assumed that 
the motion or rest of the body did not alter the relative 
position of these molecules. Thus, in falling bodies, and in 
the pendulum, we considered only the motion that was com- 
mon to the entire mass. The molecules which made up the 
moving body did not change their relative positions, and 
were, therefore, at rest with respect to each other. 

190. The following chapters relate to motion among the 
molecules of a body, but which involve the entire mass of 
the body. These molecular movements sometimes cause a 
visible change in the position of the body, but more fre- 
quently do not produce any motion in the body taken as a 
whole that we are able to detect by our senses. We know 
that these molecular motions exist by the results of the 
motion, just as we know that the hour-hand of a clock, or a 
rifle bullet, has moved by the result of the gross motion ; 
for our senses do not enable us to detect very slow nor very 
(128) 



UNDULATIONS OF SOLIDS. 129 

swift motions. When a body expands by heat, we are con- 
vinced that the result is due somehow to a motion among the 
molecules of the body. It would be difficult to keep any 
body at the same temperature all the time ; and if the tem- 
perature varies, the rate of molecular motion is increased or 
diminished, and the body is growing larger or smaller. It 
would be still more difficult to find a body that did not have 
some motion among its molecules due to the energy of heat, 
that is, that was in a state of absolute cold. Hence, on this 
consideration alone, it is probable that the molecules of even 
the most rigid bodies are constantly in motion even while 
the body, as a whole, appears to be in a state of rest. 

191. A pendulum vibrates as a whole. The times of its 
vibrations are said to be isochronous ; that is, they = 
are performed in equal times. If an elastic body 
is bent, its molecules must have changed their rela- 
tive positions, because the shape of the body is al- E\-\~AD 
tered. If, now, it is let go, the molecules will tend \ 
to assume their original positions, and, by reason of \ 
their elastic force, a series of vibrations will follow, AQ 
which are also isochronous. To show this, suspend FlG - 113 - 
a rubber tube from a hook, and stretch it taut by the hand. 
Now, if the cord be plucked at the center, it will vibrate in 
the dotted lines shown in the figure, and pass from D to E 
in precisely equal times, until it finally comes to rest. Such 
vibrations are called transverse vibrations. The greater the 
disturbing force, the greater will be the distance ED. This 
distance is called the amplitude of the vibration. The greater 
the amplitude, the greater will be the energy of the vibra- 
tion, but the time required for a vibration is unchanged. 

If, now, the cord be stretched by a weight, A, and the 
weight be pulled down and then suddenly let go, the cord 
will perform a series of longitudinal vibrations, which are also 



130 ELEMENTS OF PHYSICS. 

isochronous. That is, the weight, A, will oscillate alter- 
nately above and below its normal position, while the cord 
becomes alternately shorter and longer. So, if we twist the 
weight around, it will turn backward and forward in a 
series of isochronous torsional vibrations. 

192. All elastic bodies may be thrown into alternating 
motions of some sort, which are due to the nature of the 
disturbing force and the elasticity of the body. If we con- 
sider the motion of only one particle, as A or E, these 
motions are called vibrations or oscillations. If we consider 
the motions of a line of particles, they are called waves or 
undulations. 

193. How undulations are formed may be shown by 
stretching a heavy rubber cord from 

a fixed point, as X, by means of A— _ x 

the hand at the other end, as at 
A. If the hand be jerked up- 
ward, an apparent movement will 
be transmitted along the cord like 
the waves on the sea. If the hand 
be jerked but once, its effect will 
be to produce the crest, A E N; 
the" 'elastic force of the cord will 
cause the corresponding hollow, 
ND 0. The curve, A END 0, 
will advance along the cord, as- 
suming successively the positions 
I, II, III, until it reaches the end, X, and then return in an 
inverted curve, IV, V, VI, to the hand. The curve, 
A E N D 0, is called a wave. 

194. The particles of the cord appear to move from 
one end of the cord to the other. This, however, is impos 




FORMATION OF UNDULATIONS. 131 

sible ; each particle has moved only up and down, and the 
wave is due to a series of particles which are passing in suc- 
cession from the highest to the lowest point of the wave. 
Such a wave is called a progressive undulation. 
A is the length of the wave. E 

H E is the heiqht of the wave. ^^T^X — ■?-— -n 

D P is the depth of the wave. D 

HE-{-DPis the amplitude of the wave. FlG - 115 * 

A E N is called the phase of elevation of the wave. 
ND is called the phase of depression of the wave. 

If a pebble be dropped in a placid pool, progressive undu- 
lations will be formed. The waves w T ill spread in widening 
circles around the pebble, and decrease in amplitude as they 
increase in diameter, until they finally become inappreciable. 
As in the case of the cord, the motion of each particle is 
only up and down, as is proved by the rise and fall of 
bodies floating upon the surface. A progressive undulation 
is, therefore, only an advancing form, and any apparent pro- 
gression of the particles in the wave is merely an optical 
illusion. 

195. The surface waves o£ fluids are propagated by 
gravity. All other waves are dependent, mainly, on # the 
elastic force developed in a body by some disturbing force. 
Undulations may be confined to the body in which they are 
formed, or they may be formed in one body and transmitted 
through several others. So the vibrations of solids may 
cause waves to be transmitted to other solids, to the atmos- 
phere, or to water. Any body through which waves are 
transmitted is called a medium. 

196. Surface waves have a crest and hollow, or an up and 
down motion, but there are also waves in which the 
motion of the particle is in the same line as that of the 



132 



ELEMENTS OF PHYSICS. 



direction in which the wave is transmitted. Thus, if the 
piston in the weight-lifter, Fig. 102, is pulled down and the 
pressure suddenly removed, the elasticity of the air will 




Fig. 116. 
cause the piston to vibrate up and down. This must be due 
to the alternate condensation and rarefaction of the air 
above and below the piston. The undulations in aeriform 
bodies are chiefly due to similar waves of condensation and 
rarefaction, in which the same particle may be considered as 
moving backward and forward instead of up and down. 

197. Let a soap-bubble containing a mixture of oxygen 
and hydrogen be exploded by the flame of a candle. The 
vapor formed by the union of these elements forms a sphere 
many times greater than the soap-bubble, and thus a rare- 
faction will be produced at the center of disturbance. The 
pressure of the surrounding air will then cause the vapor 



AERIAL UNDULATIONS. 133 

.sphere to contract, its elasticity will again impel it outward, 
" and thus it will continue to oscillate by alternate rarefaction 
and condensation for some time. 

The surrounding particles of air will partake of these 
motions. When the vapor sphere expands, the shell of air 
inclosing it will be condensed, and again expand as the 
vapor contracts. This aerial shell will, in like manner, act 
upon a second aerial shell ; it, in turn, upon a third, and 
so on. 

These movements are analogous to the waves upon the 
surface of liquids, in that they increase in circumference 
from the center ; only instead of a crest Ave have condensa- 
tion, and, instead of a hollow, a rarefaction. While a sur- 
face wave consists of a crest and a hollow- ; an aerial wave 
consists of a condensation and a rarefaction. Fig. 116 is an 
attempt to represent to the eye four aerial waves : the darker 
parts represent condensations, the lighter the rarefactions. 

198. Surface waves, starting from a center of disturb- 
ance, decrease in intensity, because, as the circles widen, 
there are more particles to be moved, and each will move 
with a less amplitude. Aerial waves form spherical sur- 
faces, and, as they expand, the number of particles to be set 
in motion will increase as the squares of their radii ; hence 
their intensity will decrease in the same ratio — or, the inten- 
sity of an aerial reave diminishes as the square of the distance 
from the center of propagation increases. 

199. It will be easily understood that the greater the 
intensity of an aerial wave, the greater will be the amount 
of condensation and of rarefaction. The amplitude of an 
aerial w r ave is the space through which any particle passes 
from a state of condensation to a state of rarefaction, and 
hence the amplitude will increase w 7 ith the intensity of the 
wave. On the other hand, the length of the wave will de- 



134 ELEMENTS OF PHYSICS. 

pend on the number of particles which constitute one con- 
densation plus one rarefaction. Hence the amplitude of a 
vibration may be only a small fraction of an inch, while 
the length of an undulation may be many feet. 

200. Suppose an impulse to be communicated through 
one thousand feet in one second by means of waves. This 
will express the velocity of the wave motion. Now, the 
greater the amplitude the greater will be the resistance to 
be overcome ; the less the amplitude the less the resistance, 
and, hence, all the ivaves will move over equal spaces with equal 
velocities. The length of the wave depends on the rapidity 
with which the waves succeed each other; that is, on the 
rapidity of the vibrations or impulses which produce the 
waves. The more rapid the vibrations, the greater the 
number of waves and the shorter the wave length ; the 
slower the vibrations, the smaller the number of waves and 
the greater the wave length. Hence we may determine a 
wave length by dividing its velocity of transmission by the 
number of vibrations performed in the same time. 

Eecapitulation. 

There are two varieties of waves : 

I. Waves of crests and hollows, in which the directipn of displace- 
ment is perpendicular to that of transmission. This is exemplified by 
waves of water, the undulations of light and heat. 

II. Waves of condensation and rarefaction, in which the direction 
of displacement coincides with that of transmission. The vibrations 
of musical instruments are transmitted through the air by waves of 
this sort to the ear. These are, therefore, called sonorous waves. 

The intensity of a wave is dependent on the energy of the disturb- 
ing force. The initial amplitude is dependent on the intensity. 

The velocity of a wave is the rapidity with which it is propagated 
in a medium. 

The length of a wave is dependent both on the velocity and the 
number of vibrations in one second. 



CHAPTER XIII. 

ACOUSTICS, OR THE PHENOMENA OF SOUND. 

201. Three conditions are necessary for the sensation of 
sound : 

(1) Every species of sound may be traced to the vibra- 
tions of some elastic body. 

When a tuning-fork sounds, its vibrations may be felt by 
placing one of its prongs lightly upon the teeth. If a knife- 
blade be placed against the edge of a bell that is ringing, 
it will be made to rattle. The tremors produced in the ex- 
ternal air by the vibrations of an organ-pipe are distinctly 
perceptible. Bodies capable of producing sound are called 
sonorous. 

(2) An elastic medium is requisite for the transmission 
of sound. The ordinary medium is the atmosphere. 

The vibrations of sonorous bodies produce in the air, waves 
of condensation and rarefaction, which correspond in rapidity 
and amplitude to the rapidity and amplitude of the vibra- 
tions. These w r aves succeed each other in ever increasing 
spheres, until at last they reach the ear. Two or more 
media may be employed in transmitting the same sonorous 
wave ; thus persons in a close room are sensible of distant 
sounds. In such a case, the undulations of the external air 
cause vibrations in the windows and walls, which produce 
corresponding undulations in the air within the room. 

If a bell, kept in constant vibration by clock-w r ork, is 
supported on a thick layer of loose cotton, under the re- 
ceiver of an air-pump, the sound, at first distinct, grows 

(135) 



136 



ELEMENTS OF PHYSICS. 



more feeble as the air is exhausted, and finally ceases to be 

heard when a vacuum is obtained. Fig. 117. In like manner 

sound is quenched by theinterpo- 

sition of any body having feeble 

elasticity. Thus, a partition filled 

with sawdust, or covered by 

a thick carpet, will prevent the 

transmission of sound from one 

room to another. 

(3) The auditory nerve is neces- 
sary to the sensation of sound. 

If ~*he experimenter is deaf, or 
if a bell rings when there are no 
hearing organs capable of per- 
ceiving the vibrations, they ex- 
ist merely as such, without pro- 
ducing sensation. 

Nevertheless, in studying these 
vibrations it is convenient to dis- 
regard the sensation, and define sound as a mode of motion 
which is capable of affecting the auditory nerve. 

202. A musical sound is produced by vibrations which 
succeed each other at short and equal intervals. If the 
vibrations are rapid, the ear recognizes the sound as high or 
acute ; but, if slow, as low or grave. 

These facts may be shown by pressing a card against a 
toothed wheel in motion. Fig. 118 represents Savart's 
wheel. If the card, E, strikes against less than 16 teeth 
per second, only a succession of taps will be heard. If the 
number exceeds 16 per second, the impulses blend together 
in a clear musical sound. As the velocity is increased, the 
sound is more and more acute. Therefore, the pitch or tone 
depends on the rapidity of the vibrations, Savart's wheel has 




Fig. 117. 



SAVARTS WHEEL. 



137 



at H an apparatus which indicates the number of revolu- 
tions in the toothed wheel by which we can easily calculate 
the number of vibrations per second that are required to' 




Fig. 118. 
produce any given tone. Sounds are in unison when the 
rates of vibration are the same. We may determine the 
rate of vibration in tuning-forks and other musical instru- 
ments by making the wheel sound in unison with them, and 
then noting the rapidity of the vibrations produced by it. 

If the vibrations are less than 16 per second, the ear is 
affected by each impulse separately, and only a noise, or a suc- 
cession of noises, is heard. 

203. The quality of sound depends on the elasticity and 
form of the sounding body. Steel, glass, silver, brass, and 
cat-gut, are sonorous, because these substances are highly 
elastic, and possess sufficient strength for rapid vibrations. 
The fibers of wool and cotton are elastic, but are not sonor- 
ous, because their elasticity is so feeble that their vibrations 
are slow and inaudible. Hence, all elastic bodies are not 
sonorous, although all sonorous bodies are elastic. 

204. If a tuning-fork be struck by a sharp blow, its 
sound will be at first loud, and then gradually die away. 

Phys. 



138 ELEMENTS OF PHYSICS. 

The blow causes vibrations in its prongs that have consid- 
erable amplitude; the greater this amplitude, the greater 
will be the condensation which it produces in the aerial 
wave. As the amplitude decreases the condensation is less, 
until finally the condensation is not sufficient to affect the 
ear. Hence, the intensity or loudness of the sound depends on 
the amplitude of the vibrations. It must not be forgotten that 
the loudness has nothing to do with the pitch of a tone; 
thus, the same tuning-fork always vibrates w T ith the same 
rapidity and yields the same tone, whether that tone be 
loud or soft. 

The amplitude of sonorous waves rapidly decreases, be- 
cause they are propagated in spherical surfaces ; hence, the 
intensity of sound varies inversely as the square of the distance of 
the sounding body. A drum at a distance of one hundred 
feet sounds four times louder than at two hundred feet, and 
one hundred times louder than at one thousand feet. 

205. When a string vibrates in free air, it emits but a 
feeble sound ; but if it is fastened to a violin or a suitable 
sounding-box, the sound is louder. This arises from the fact 
that the thin plates of the box and the air within them vibrate 
in unison with the string, and the united effect is to produce 
a wave of greater intensity. We may illustrate this by 
holding a vibrating tuning-fork over the mouth of a tall jar, 
and carefully pouring water into the jar. Fig. 119. When it 
has reached a certain level, the sound of the fork will be 
greatly increased by the vibration of the column of air 
within the jar. The best effect will be produced when the 
length of the air column is such that a wave of condensa- 
tion or of rarefaction will go down and back while the 
tuning-fork is making a single vibration. That is, the 
length of the column should be one-fourth of the length 
of the sonorous wave produced by the fork. "We learn from 



INTENSITY OF SOUND. 



139 



these experiments that sound is increased in intensity by the 
proximity of a resonant body. 

206. These experiments 
show that a vibrating body 
is capable of exciting undu- 
lations in bodies whose rate 
of vibration is the same as 
its own. When the voice 
utters a prolonged loud tone 
near a piano, that wire will 
be set in vibration whose 
sound is in unison with the 
voice. Such vibrations are 
termed sympathetic. Only 
that wire answers to the 
voice that, is capable of emit- 
ting the same tone when it is 
struck FiaTm" 

207. The intensity of sound depends on the density of 
the medium in which it is generated. The experiment of 
the bell in vacuo shows that the more the air is rarefied, the 
weaker is the sound. On the tops of mountains the sound 
of a pistol resembles the report of a fire-cracker ; while a 
whisper sounds painfully loud to the occupants of a diving- 
bell. The energy with which solids and liquids transmit 
sound exceeds that of the atmosphere. The scratch of a pin 
at the end of a long stick of timber is distinct to a person 
whose ear is at the other end. 

208. The intensity of sound is weakened in passing 
from one medium to another. A noise made under water 
is feebly heard in the air, and vice versa. If the lungs are 
filled *vith hydrogen, the voice is weak and piping. The 




140 ELEMENTS OF PHYSICS. 

reason why sounds are more distinct by night than by 
day is because the air is more homogeneous. In the day- 
time the air contains layers of different densities, and the 
sound is weakened both as it enters and as it leaves one of 
these layers. 

209. The distance at which sound is audible varies 
with the conditions that determine its intensity. Still air 
of great density and uniform temperature is favorable to 
the transmission of sound. In the Arctic regions, Lieuten- 
ant Foster conversed with a sailor at the distance of a mile 
and a quarter. The earth transmits sound further than air. 
The cannonading at Antwerp in 1832 was heard in the mines 
of Saxony, 320 miles distant. 

210. The velocity of sound. Every one must have no- 
ticed that the flash of a distant gun is seen before the 
report is heard. If the distance and the time between the 
flash and the report are known, the velocity of sound may 
be computed. The velocity of sound in still air at 32° F. 
is 1090 feet per second. 

211. The velocity varies with the temperature, increas- 
ing, as the temperature rises, at the rate of ..1.12 feet for 
every degree Fahrenheit. At 60° F. sound has a velocity 
of 1121 feet per second. 

212. These facts enable us to compute the distance of a 
sounding body when the time of transmission is known. 
Thus : suppose, on dropping a stone from a cliff, eight sec- 
onds elapse before the stone is heard to strike the base. A 
part of the time, x, was occupied by the falling body, the 
rest, 8 — x, by the sound. By the law of falling bodies 
x 2 X 16^ equals the height of the cliff; by the law of the 
transmission of sound (8 — x) 1090 also equals the height. 
Hence, x 2 X 16 T V = (8 — x) 1090. # = 7.23; 8 — z = 0.77. 
The height of the cliff is, therefore, 839.7 feet. 



THE VELOCITY OF SOUND. 141 

213. All sounds are transmitted with the same velocity 
in the same medium. If this were not true, the different 
notes simultaneously produced by the instruments of an 
orchestra would reach the ear of a distant auditor one after 
another, and so produce discord. 

214. The velocity of sound varies with the medium. 
In gases denser than air, it moves with less velocity; and 
in those rarer, w T ith greater velocity: in carbonic acid, the 
rate is 858 feet, and in hydrogen 4,164 feet per second. In 
solids and liquids, the velocity is greater than in air; in 
water, the rate per second is 4,700 feet; in lead, 4,030 
feet; in steel and glass, 16,600 feet; in ash, 15,314 feet. 

The difference of velocity in solids and in air may be demon- 
strated by placing the ear at one end of a long beam or wall, 
while an assistant strikes a blow at the other end. Two sounds 
will reach the ear, the first through the solid and the other 
through the air. 

215. If the sonorous wave is not permitted to expand, 
its intensity can be maintained for a great distance. The 
speaking-tubes employed in large buildings for transmitting 
messages from one story to another illustrate this fact. The 
hearing trumpet concentrates sound, because the condensa- 
tion and rarefaction of the sonorous wave w r hich enters it 
is communicated to portions of air which are smaller and 
smaller, and thereby the intensity is increased. 

215a. Edison's phonograph is an interesting proof that sounds 
are due to vibrations. It consists of an elastic plate, to the center 
of which a hard stylus is so attached that it plays above a sheet 
of tin-foil, which is made to cover a cylinder whose surface is 
cut into the form of a screw. On turning the cylinder, and at 
the same time speaking at the elastic plate, the stylus forms in- 
dentations in the tin-foil which correspond to the sounds uttered. 
After the tin-foil has been indented, if the cylinder is revolved as 
before, the sounds will be reproduced by the elastic membrane 
with greater or less fidelity. 



142 



ELEMENTS OF PHYSICS. 



Sonorous Waves. 



216. Many sounds may be transmitted at the same 
time in the same medium without modifying each other. 
A cultivated ear can readily distinguish the sound of each 
different kind of instrument in a large orchestra. If, how- 
ever, there are many instruments of the same kind perfectly 
in unison, their sounds will unite to produce a resultant 
wave of increased intensity. So, also, many feeble sounds, 
separately inaudible, may unite to produce a sort of mur- 
mur, as is exemplified by the rustle of leaves, or the hum 
of a whispering school. 

217. If two sonorous waves of equal intensity combine, 




Fig. 120. 
the effect may be either to increase or diminish their inten- 
sity. We can readily illustrate this effect by means of a 
long, narrow canal, with glass sides, partially filled with 
water. On tilting one end, a wave will pass to the other 
end, and be there reflected. If new waves are formed by 
fresh impulses, we may so time the motion that the direct 
and reflected waves may be made to meet at any phase of 
their undulation. If crest combine with crest and hollow with 
hollow, the amplitude of the resultant wave will be doubled ; 
but if crest combine with hollow, both waves will disappear, 
and the surface become horizontal. This phenomenon is 
called the interference of waves. 

In like manner, if two sonorous waves of equal intensity 
meet in opposite phases, so that the condensation of one 



INTERFERENCE OF WAVES. 143 

corresponds with the rarefaction of the other, both are de- 
stroyed, and silence results. The feeble sound of a tuning- 
fork, held in the hand, is partially due to the fact that the 
prongs are vibrating in opposite directions, and produce 
a partial interference of their waves. If a tuning-fork, when 
vibrating, is turned slowly around about a foot from the ear, 
four positions will be found in which the interference is 
total, and no sound is heard. 

If two tuning-forks, vibrating respectively two hundred 
and fifty-five and two hundred and fifty-six times in a sec- 
ond, are sounded together, they will, at first, combine to 
produce a louder sound than either could alone, for both 
generate waves in which condensation corresponds with con- 
densation, and rarefaction with rarefaction. At the one 
hundred and twenty-eighth vibration, one will have gained 
half a vibration on the other, and their phases are in com- 
plete opposition, and there will be no sound, because the 
condensation of one wave is neutralized by the rarefaction 
of the other. For the next half second, the interference is 
less and less, and at the end of the second they again com- 
bine. At every even number of half seconds the sound will 
be doubled in intensity, and at every odd number destroyed. 

This alternate combination and interference is known to 
musicians by the name of beats. The number of beats in 
a second is always equal to the difference in the two rates of 
vibration. If the forks vibrate in unison no beats will be 
heard. If one vibrates two hundred and fifty and the other 
vibrates two hundred and fifty-six times in a second, the 
number of beats will be six. 

218. Echoes are produced by the reflection of sound from 
distant surfaces. 

Let a circular wave emanate from the center, 0, and 
strike the plane surface, S B, with a velocity sufficient to 



144 



ELEMENTS OF FHYSICS. 








*f A 


y 




,4/ 


V K fr i 


;\E/ 




^i 


V 
0' 





B 



Fig. 121. 



have carried it in the next moment to S P B. The parti- 
cles in the perpendicular ray, 0', will first strike the sur- 
face, and will be reflected in the direction, 0' P. When any 
diverging rays, as U and 
01 reach the surface, they 
will be reflected on the other 
side of the perpendiculars, 
MK and W E, in the lines, 
O'D and 0' I, making the s 
angles of reflection equal to 
the angles of incidence. Now, 
as the velocities of the direct 
and the reflected waves are 
the same, the reflected wave 
will reach the points, DPI, in the same time that the 
direct wave would have reached U P I, and the same 
is true of all intermediate points. Hence, the reflected 
wave proceeds as if from a center, 0', on the opposite side 
of the surface, SB, and at a distance from the surface 
equal to that of the center, 0, of the incident wave. 

When the origin of the wave is far distant from the re- 
flecting surface, the waves will be arcs of very large circles. 
In such cases, the diverging rays which fall upon a small 
surface will be nearly parallel. Parallel rays, incident upon 
a plane surface, will also be parallel after reflection. 

Echo. The voice can not utter, nor the ear hear, more 
than five syllables in a second ; therefore, a distinct echo of 
articulate sounds will require the reflecting surface to be at 
least 1090 -f- (5 X 2) = 109 feet distant, as the sound has 
both to go from and return to the speaker. At a greater 
distance, two or more syllables may be perfectly repeated 
by the echo ; but, at less distances, the direct and reflected 
waves will be more or less commingled, and the echo will 
not be distinct. 



RESONANCE. 145 

219. The increased intensity produced by the com- 
mingling of direct and reflected waves is termed resonance. 
Resonance is specially noticeable in empty rooms with bare, 
smooth walls. If the echoing walls are not distant more 
than thirty-five feet from the speaker, the reflected wave 
will reach the ear one-sixteenth of a second after the direct 
wave. This very short interval will not be noticed by the 
ear, and the voice will be strengthened without a loss of 
clearness. If the walls are at a greater distance the words 
are less distinct, unless the echoes are quenched by the fur- 
niture, or by the presence of an audience. 

220. The echo may be heard 
when the direct sound is inaudi- 
ble. Thus, if two concave mir- 
rors are placed opposite to each 
other, the ticking of a watch 
placed in the focus of one mirror 
will be so reflected that it may be 
heard in the focus of the other, FlG - 122 - 

even when placed at a considerable distance. Fig. 122. 
The same effect may be produced in circular rooms. In 
such a chamber, a whisper at one focus will be heard at the 
other focus, although inaudible at any other place. Such 
whispering galleries are not uncommon. The dome of St. 
Paul's Cathedral, London, and of the Capitol at Washing- 
ton, are fine examples. 

221. Sound may be bent out of its course or refracted in 
passing from one medium to another. The laws of refracted 
sound are the same as those of light, and will be studied 
hereafter. 



Phys. 13. 




146 ELEMENTS OF PHYSICS. 

Recapitulation. 

1. The quality of sound depends on the elasticity and form of the 
sonorous body. 

2. The pitch of sound depends on the rate of vibrations. 

3. The intensity of sound increases: (1.) With the amplitude of 
the vibrations. (2.) With the density of the generating medium. 
(3.) By the proximity of a resonant body. 

The intensity of sound decreases: (1.) As the square of the dis- 
tance increases. (2.) In passing from one medium to another. 

The intensity is maintained or strengthened by acoustic tubes. 

4. The velocity of sound is not dependent on quality, pitch, or 
intensity, but varies with the elasticity and density of the medium. 

!(1) may co-exist in the same medium. 
(2) may combine and interfere. 
(3) may be reflected or refracted. 



Musical Sounds. 



222. The appreciation of musical sounds varies in 
different persons. Some can hardly distinguish variations 
in pitch, although they are sensible to variations in inten- 
sity. All ears are deaf to some vibrations. The gravest 
sound is produced by 16 vibrations per second, the highest 
sound by 38,000 vibrations per second ; but there are many 
persons who can not hear very high notes like the note of a 
cricket, although they can distinguish very feeble sounds, as 
the lowest whisper. 

223. More than 38,000 sound waves are possible, each 
one of which will, by itself, produce a pure tone. No ear is 
capable of recognizing, as distinct tones, one-hundredth part 
of these. Two tones, whose rates of vibration are nearly 
the same, can be distinguished from unison only by the for- 



MUSICAL SOUNDS. 147 

mation of beats. If these beats are not readily perceptible, 
the ear recognizes the sound as the same. 

224. Suppose a guitar string to be stretched across a 
sounding box, as in Fig. 123. When the whole length of 




Fig. 123. 

the string vibrates, it produces a sound called the funda- 
mental tone of the string. Suppose this tone to be that due 
to 128 vibrations in one second, as measured by Savart's 
wheel. If, now, the bridge, jB, be placed at half the length 
of the string, it will make 256 vibrations per second, or 
twice as many as the fundamental. If the string be again 
halved, the number of vibrations will be again doubled, 
and so on. 

The ratio between any two tones is called an interval, and 
indicates how much one sound is higher than another. The 
interval 1 : 2 is called an octave, because, between any two 
tones bearing this ratio, other tones may be placed, so as to 
form, with the two extremes, a series of eight sounds hav 
ing agreeable relations to each other. 

225. These eight tones constitute the diatonic scale or 
gamut. They are designated by the first seven letters of the 
alphabet. If the length of the string which sounds the fun- 
damental be assumed as 1, the relative length required to 
produce the other tones are : 



4 
5 


1 


2 
3 


3 
5 


8 
T5^ 


1 
2 


5 
4 


4 
3 


3 

2 


5 
3 


15 

8 


2 



148 ELEMENTS OF PHYSICS. 

Tones. . . CDEFGABC 

Relative length of cord. . . 1 
Relative number of vibrations. 1 

The laws which govern the vibrations of strings are : 

(1) The number of vibrations per second is inversely pro- 
portional to the length of the string. 

(2) The number of vibrations per second varies as the 
square root of the weight by which the string is stretched. 

(3) The number of vibrations per second varies inversely 
as the square root of the weight of a given length of string. 

All these laws are applied in the construction of stringed 
instruments. The high notes on a piano are produced by 
short, thin strings ; the low notes by long heavy ones. The 
strings are brought to the proper pitch by tension, applied 
at the pegs. 

226. Musicians have agreed to designate the tone due to 
128 vibrations per second as C. It corresponds to G in the 
second space of the base clef. The number of vibrations 
corresponding to any other tone may be found by multiply- 
ing this number by the fractions ■§-, f , etc., which express the 
relative number. The actual number employed by orches- 
tras in different cities is not the same. For this reason a 
new scale of vibrations has been proposed, which give all 
the tones of the lower octave of the treble in whole num- 
bers, C 2 being 264. 

227. The length of a sonorous wave is found by divid- 
ing the velocity with which sound travels in a second by the 
number of vibrations per second. In air, at 60° F., the 
length of the wave, C, is 1,121 --128 = 8.7 feet. 

228. Musical intervals are named by the order of their 
position with respect to the fundamental, as seconds, thirds, 
fourths, etc. The interval of the fifth, as CG or 6?D 2 , is 



MUSICAL SCALE. 



149 



expressed by the ratio 3 : 2. The following table gives a 
condensed summary of the relations of two octaves of the 
diatonic scale : 







I ! 



-rfel 



<- 

o - 

N 
fa" 

ft- 

o - 

< 

fa" 

fa" 

ft 

O - 



-8 



-fcl 



UN. 



•3 © » 

x Q ^ i- 



CO -vi 



C2 -~ 
O cc 

fa *k? 

M 

ft .*N< 

ft > 

<r 4, 

cT mm 
fa r< 
fa 
ft 



CO (M 

'a * 

CO CO 

s "? 

CO CO 



c_ OC 

J* CO 

0<l 



0*c CO 



r*:« T— I 



CO 



OC 


!§j 


fa.,^2 






M 3- « 

ft -N 2 



C|ac CO 



l-H O 

o 
o 
1-1 t— 



CO l . 

r^ CO 



,C c3 



s * 



c3 



P 



c5 ^ 



« £ 



^ h3 



150 



ELEMENTS OF PHYSICS. 



229. The pleasure derived from music depends on the 
frequent recurrence of vibrations in the same phase. Melody 
is due to a succession of simple tones having agreeable rela- 
tions to each other. The air in a piece of music is an ex- 




FlG. 124 

ample of melody. A chord is due to the simultaneous pro- 
duction of two or more tones in agreeable relations to each 
other. A harmony is a melodious succession of chords. The 
air in music, with the accompaniment, constitutes a har- 
mony. 

Music is often composed and executed without any knowl- 
edge of sonorous waves, because the ear almost instinctively 
recognizes the combinations that are agreeable. When these 
combinations are analyzed, it is found that those are most 
agreeable whose vibrations bear simple relations to each 
other. If the ratio between any two sets of vibrations can 
be expressed by whole numbers less than six, the combina- 
tion will be pleasant. Such are notes in unison, 1:1; then 
the chords of the octave, 1:2; then follow, in turn, the 
chords of the fifth, 2 : 3, the fourth, 3 : 4, and so on. 

230. A string which vibrates transversely along its 
whole length can be made to vibrate in any number of 
segments by gently touching it at any aliquot part of its 
length, as one-half, one-third, etc., either at the moment the 



NODAL LINES. 



151 




Fig. 125. 



string is set in motion or after it has begun to vibrate. The 
touch quenches the vibration at the point, and the string 
divides into two, three, or 
more segments according 
to the distance of the 
point touched from the 
end. Now, not only will 
the vibration cease at the 
point touched, but also 
the string will be at rest 
between every two seg- 
ments. If rings of paper 
are placed along the string 
they will collect at these 
points of rest, w T hich are 
called nodes. Fig. 124. 

It is impossible to sound the string as a whole without, at 
the same time, producing some vibrations of its aliquot 
parts. The string will, therefore, yield its fundamental tone 
strongly and some of its higher harmonics with less inten- 
sity. The same is true of other sounding bodies. This in- 
termixture of tones gives each instrument a peculiar quality, 
called timbre, which enables us to distinguish one instrument 
from another, as a violin from a flute. 

231. When plates are set in vibration nodal lines are 
formed. These may be rendered evident to the eye by cov- 
ering the plate with fine sand. On quenching the vibration 
at any point, the sand will gather at the positions of rest 
and form beautiful symmetrical figures, as shown in Fig. 125. 

If a thin goblet be partially filled with water, and then 
rubbed on the edge with a wet finger, the glass will emit a 
musical tone, and waves and nodal lines will be formed on 
the surface of the water. 



152 



ELEMENTS OF PHYSICS. 



232. In wind-instruments the sound 
column of air which is confined 
in the tube. Fig. 126 represents 
an organ-pipe. When a blast of 
air is forced through the aperture, 
I, it strikes against the lip, b, which 
partially obstructs it and causes the 
air to issue from ba in an intermit- 
tent manner. In this way pulsations 
are produced, which cause alternate 
condensations and rarefactions within 
the tube, and a sonorous wave is the 
result. 



is due 




to the 



Fig. 126. 



Recapitulation. 



1. Any sonorous body gives its fundamental tone when it is vibra- 
ting throughout its whole length. 

2. The diatonic scale contains eight tones of different intervals. 

3. The relative number of vibrations in an octave is expressed by 
a simple series of ratios. The corresponding tones may be obtained 
by varying the length, tension, and weight of strings. 

4. The pleasure derived from music is due to a succession of 
melodious or harmonious tones. 



CHAPTER XIV. 

OPTICS, OK THE PHENOMENA OF LIGHT. 

233. Luminous bodies are those in which light origi- 
nates ; all others are non-luminous. Thus, the sun and burn- 
ing bodies are luminous. Trees and stones are non-luminous, 
but while the sunlight falls upon them they give off part of 
the light which they receive, precisely as if they were 
luminous bodies. 

234. Transparent bodies allow 7 light to pass freely 
through them ; as glass, water, air. Opaque bodies do not 
transmit light ; as wood and the metals. Translucent bodies 
transmit light so imperfectly that objects can not be clearly 
seen through them ; as ground glass or horn. 

235. The sun and the fixed stars originate the light by 
which they shine ; the planets and the moon shine by the 
light which they receive from the sun. (1) These are nat- 
ural sources of light. 

When any solid is sufficiently heated it emits light, and is 
said to become incandescent The light varies with the inten- 
sity of the heat. At 977° F. bodies emit light of a dull red 
color; at 1,280° F. they are red-hot; at 2,000° F. orange; 
at 2,130° F. white hot, and above this temperature they 
are dazzling w T hite. Hence,, any source of intense heat will 
also be a source of light, if there are solid particles present 
which can be rendered incandescent. 

(2) Chemical action is the principal source of artificial 
heat and of artificial light. AVhen oxygen and hydrogen 
are burned together, a temperature of over 5,000° F. may 

(153) 



154 ELEMENTS OF PHYSICS. 

be attained. If the two gases alone are present the light is 
very feeble, because the product of combustion is aeriform, 
viz. : the vapor of water. If, however, a solid, as a bit of 
iime, is held in the flame, it becomes incandescent, and 
emits a light of great intensity. It is the so-called calcium 
or Drummond light. 

The common illuminating agents, like oil, tallow, coal gas, 
etc., contain carbon and hydrogen. When these bodies are 
ignited, they are decomposed ; the hydrogen burns with a 
pale flame ; into this flame the solid carbon particles rise, 
become incandescent, and emit light. They then burn and 
pass into the air as carbonic acid. 

Besides these sources of light may be mentioned (3) me- 
chanical action, exemplified by the sparks of light emitted 
when flint and steel are struck violently together, (4) elec- 
tricity, as in the glare of lightning, (5) and the phosphores- 
cent light emitted by decaying wood, and by some insects. 

' 236. The phenomena of light may be explained by the 
theory that it is due to very small waves of crests and hol- 
lows. The wave theory of light assumes (1) that matter of 
extreme rarity and elasticity, called the luminiferous aether, 
pervades all space, even the interstices between the molecules 
of every substance. (2) That the molecules of luminous 
bodies are in a state of very rapid vibration. (3) That the 
vibrations of every luminous point are communicated to the 
aether, and are then transmitted in all directions by spherical 
waves. (4) That these vibrations or waves constitute 
light. 

237. The velocity of light was first ascertained by 
Roemer by means of the eclipses of the first moon of the 
planet Jupiter. This moon is observed to undergo eclipses 
by passing behind the body of the planet. Both the earth 
and Jupiter revolve about the sun, but in different periods ; 



VELOCITY OF LIGHT. 155 

consequently, they are sometimes on the same side of the 
sun, and sometimes on opposite sides. In the former case 
the earth is the whole diameter of its orbit, or about 183, 
000,000 miles, nearer to Jupiter than in the latter. Now, as 
the moon of Jupiter has a uniform time of revolution about 
the planet, its times of eclipses should also be uniform if 
light passed instantaneously ; but Roemer found that the 
eclipse of the moon is seen 16f-§ minutes sooner when the 
earth is nearest to Jupiter than when it is furthest from 
him ; therefore, the light must occupy this time in crossing 
the earth's orbit. The velocity is then about 185,500 miles 
in a second. 

The velocity of light has since been calculated by direct 
experiment, and found to vary in different media ; being in 
water 144,000 miles per second; in glass, 128,000 miles; 
in diamond, 77,000 miles. 

238. Luminous bodies may be considered as a collection 
of luminous points. In the study of light it is convenient 
to assume, unless the contrary is stated, that the source of 
light is a luminous point. Suppose we had a very small 
bit of incandescent lime, it is evident that we could see it 
in all positions of the eye if there were no opaque body 
intervening ; hence, light radiates in all directions from a 
luminous point 

A single line of light is called a ray. A collection of 
rays from the same source is called a pencil of light. The 
rays of light emanating from a point tend to separate from 
each other, and thus form divergent pencils ; but, if the point 
is very distant, the rays that enter the eye will be sensibly 
parallel, and, hence, will form a pencil of parallel rays or 
a beam of light. Finally, we may so modify either divergent 
or parallel pencils that they will become a convergent 'pencil, 
that is, one whose rays are directed to a common point. 



156 



ELEMENTS OF PHYSICS. 



A— 



239. Light moves in straight lines through a homoge- 
neous medium. A ray of sunlight admitted into a dark 
room is seen to be straight by illuminating the floating 
motes in its course. When an opaque body intervenes, the 
light is cut off, and a shadoiv is formed. If the source of 
light be a point, the shadow will be bounded by rays tan- 
gent to the opaque body. Gen- 
erally speaking, the line that 
bounds the shadow is not clearly fig. 127. 
defined, because the luminous body has a sensible mag- 
nitude. 

240. The intensity of the light varies inversely as the 
square of the distance from a luminous point. This is a 
property of all spherical waves, and may be shown experi- 
mentally for light by means of shadows. 

A board having a surface one foot square placed one foot 
from a very small candle, will cast a shadow that will cover 
four square feet at double the distance, nine square feet 
at treble the distance, and so on. The areas increase as the 

square of the distance, and, 
__ consequently, the intensity of 
light on each square inch will 
decrease in proportion to the 
square of the distance from 
the luminous point. 

241. The relative intensi- 
ties of two lights may be 
compared by an application 
of this law. Place an opaque 
rod before a vertical screen of white paper, and arrange the 
lights so that each shall cast a shadow of the rod on the 
screen. Now move one of the lights backward or forward 
until a position is obtained in which both shadows appear 




Fig. 128. 



RELATIVE INTENSITY. 157 

equally dark, If the shadows are equal, the amount of 
light foiling on the screen from each source must be equal 
also, hence the relative intensities of the two lights are 
found by squaring the distance of each light from the 
screen. In such measurements, it is usual to select a candle 
of known weight as a standard unit, the other light is then 
spoken of as having as many "candle-power" as is expressed 
by the ratio found. The light which we receive from the 
sun is equal to that of 5,563 wax candles- placed at the dis- 
tance of one foot. The light of the full moon is 300,000 
times less than that of the sun. 

242. We should not forget that these laws apply strictly 
to luminous points. We can readily see that the illumina- 
ting effect takes into account also the size of the luminous 
body. Let us suppose, for example, that each portion of a 
broad gas jet shines with equal intensity. If we cover the 
jet with a tin shade having a narrow slit in its side, the 
illuminating effect of the jet will be decreased, although the 
intensity of the light which passes through the slit will not 
be altered. So, also, a bright coal-fire may have as great 
an illuminating effect as a gas jet, although with a less 
intensity. 

243. When a pencil of light falls on any substance it 
is separated into parts. (1) Some of the light is always 
absorbed. (2) Some of the light is always reflected. (3) 
Some of the light may be transmitted. When the transmit- 
ted light is changed in direction it is said to be refracted. 

Absorption. A very thin plate of glass is almost per- 
fectly transparent, but if its thickness is increased, its 
transparency is diminished, and it may be made so thick as 
to transmit no light. On the other hand, gold may be 
made so thin that it will transmit light, The transmitted 
light has a violet-green color. 



158 



ELEMENTS OF PHYSICS. 



Recapitulation. 



I. Bodies are classified with reference to light in regard- 

j Luminous. 
\ Non-luminous. 



1. To the emission of rays : 



{Transparent. 
Translucent. 
Opaque. 



II. Light incident on a surface is: 



1. Absorbed. 

2. Reflected. 

3. Transmitted. 



Reflection of Light, or Catoptrics. 

244. If a ray of light, as IB, falls on a plane surface, 
A C, a portion of it will be reflected or thrown back in the 
line, B B. Suppose 
a line, P B, to be 
drawn from the 
point of incidence, 
perpendicular to the 
reflecting surface, 
AG. It will form 
with the incident 
and reflected rays Fig. 129. 

two angles, viz: IB P, called the angle of incidence, and 
R B P, called the angle of reflection, and in every case the 
angle of incidence is equal to the angle of reflection. 

245. If a pencil of light falls on a perfectly plane sur- 
face, the reflected rays will proceed in the same direction, 
and the light is said to be regularly reflected. When a flat 




MIRRORS. 159 

surface is examined by a microscope it is generally found to 
consist of a number of minute planes inclined to each other 
at all possible angles. Now, as each little plane has its own 
perpendicular, the light which falls on an uneven surface 
will be reflected in all directions, and is then said to be 
irregularly reflected or diffused. 

246. Non-luminous bodies are rendered visible by light 
irregularly reflected. The light which they reflect renders 
them temporarily luminous. Those bodies which are not in 
the direct sunlight are illuminated by the diffused light 
reflected from surrounding objects. If a large portion of 
the incident light is reflected regularly, the eye may per- 
ceive an image of the body which emits the light. A good 
mirror gives a bright image of objects in front of it by 
reason of the light which it reflects regularly, but is itself 
seen by light irregularly reflected. A surface that reflected 
none of the incident rays irregularly would itself be invisi- 
ble, and no substance is known that is perfectly reflecting, 
absorbing, or transparent. 

247. Mirrors are either plane or curved. A looking- 
glass is an example of a plane mirror. The most common 
kinds of curved mirrors are those w r hose curvature is spher- 
ical. A convex spherical mirror is a portion of a spherical 
surface reflecting light from the outer face ; a concave spher- 
ical mirror is a portion of a spherical surface reflecting 
light from the inner face. 

The formation of images by mirrors may be determined 
by investigating the images due to a series of points on the 
object. 

248. Plane mirrors. Let A B be an arrow in front of 
the plane mirror, M N. Fig. 130. The point, A, will emit 
a great number of rays. One pencil will be so reflected that 



160 ELEMENTS OF PHYSICS. 

it will appear to the eye to come from A! \ a pencil from B 

will appear to come from B '; the pencils from intermediate 

points on the arrow from points be- „ 

tween A' and B\ Hence, if an ob- A*%r^^\ £avye 

ject be placed before a plane mirror, 

the image will be formed behind the 

mirror. Such an image has no real 

existence, and it is called a virtual 

image, because the rays only appear 

to come from the other side of the B' I 

Fig. 130. 
mirror. 

In plane mirrors, the image is the same size of the object, 

and appears as far behind the mirror as the object is in 

front. 

249. If an object is inclined to the mirror, its image 
has an equal inclination ; hence, the inclination between the 
object and the image is double that which each has to the 
mirror. For this reason, trees appear inverted by reflection 
from the surface of water. 

If the object and mirror are parallel, there is a semi- 
inversion in one direction only. If a printed page is held 
before a plane mirror, the letters are reversed in a horizon- 
tal direction, or from right to left. If a person stands be- 
fore a vertical mirror, the image of his right hand will be 
on the left side of the image. 

Since the angles of incidence and reflection are equal, a 
person may see his entire image in a vertical mirror of half 
his length. 

250. Multiple images are formed by mirrors inclined to 
each other. Two mirrors at right angles give three images. 
If the mirrors are inclined 60°, five images are produced. 
The number of images increases as the angle is reduced, 



THE KALEIDOSCOPE. 161 

and would be infinite when the mirrors are parallel, if the 




Fig. 131. 
light w r ere not gradually weakened at each successive re- 
flection. 

251. The kaleidoscope illustrates this property of in- 
clined mirrors. It consists of a tube containing two or 
three long and narrow mirrors inclined to each other ; one 
end of the tube is closed by ground glass, and the other by 
plane glass. Small colored objects, as bits of glass, are 
placed in a cell between the ground glass and another glass 
disk, leaving just room enough for the objects to tumble 
about as the tube is turned. On looking through the tube, 
the objects and their images are seen in beautiful forms. 

252. Curved mirrors may be considered as made up of 
Q an infinite number of plane mirrors 

inclined to each other. Let TT" be 
a section of a portion of a spherical 
mirror. C is called the center of curv- 
ature. The line, CC\ which passes 
c " through the vertex of the mirror, is 
called the principal axis of the mirror ; 




162 ELEMENTS OF PHYSICS. 

any other line, as C C or CC", which passes through the 
center of curvature, is called a secondary axis. Any radius, 
as CI, is perpendicular to the concave surface, and its pro- 
longation, as IC, is perpendicular to the concave surface; 
or, what is the same thing, these radial lines are perpen- 
dicular to the little planes, T T, T T" , of which we may 
consider the mirror to be composed. 

253. In concave spherical mirrors the image formed 
on reflection varies with the distance of the object. The 
most important cases are the following: 

(1) If a luminous point is at a very great distance, its 



H- 
G- 




L CH#^ 



Fig. 133. 

rays will be sensibly parallel. Suppose the parallel rays 
HB, G D, LA, to fall upon the mirror. Any ray, as HB, 
will be reflected so that the angle H B C is equal to the 
angle CBF. All the reflected rays will pass through the 
point, F, which lies on the principal axis, about half-way 
between the mirror and the center of curvature. This point 
is called the principal focus of the mirror. 

Now, as all the rays are reflected to one point, there will 
be a concentration of light at the focus, but no image will 
be formed. The converse is also true ; if a bright point 
were placed at the focus, its reflected rays would be parallel, 
and not enough of them would enter the eye to form an 
image. Hence we may use concave mirrors to concentrate 
light to a focus, or, as in light-houses, to reflect the rays 
from a lamp placed in the focus in parallel rays. 



FORMATION OF IMAGES. 163 

(2) If the point is at a finite distance its rays will be 
divergent. Suppose L to be a point beyond the center of 
curvature, its rays will converge on reflection to a point I, 

\K 
^ \l 

Fig. 134. 
between the principal focus and the center of curvature, 
and, conversely, rays diverging from I will converge on re- 
flection to the point L. Points so related are called conju- 
gate foci. 

Now, suppose a candle to be placed at the same distance 
a^ L. The rays from the tip, J., will converge to some 
point, a, on the secondary axis, A E. The rays from B to 





Fig. 135. 



some point, 6, on the secondary axis, B I. Between these 
two extremes, the images of the other points will be formed ; 
hence, a 6 is the complete image of A B. The image is 
inverted, smaller than the object, and lies between the center 
and the principal focus. 

Reflecting telescopes are used to give a small but bright 
image of the heavenly bodies. These images are viewed 
after being enlarged by lenses. If a reflecting telescope is 
turned to the sun, the rays from any point on its surface 
will be parallel, but the rays from any two distant points, 
as the center and the edge, will not be parallel. Hence, an 



164 



ELEMENTS OF PHYSICS. 



image of the sun will be formed very near the principal 
focus of the mirror. 

Conversely, if the object were at a b the image would 
be at A B, enlarged, beyond the center, and inverted, with 
respect to the object. Both these images would be real, 
for either may be received on a screen. 

254. (3) When the object is between the principal 
focus and the mirror, a virtual image is formed, which is 
erect and enlarged. 

Let A B be an arrow nearer than the principal focus. 
Draw the axes, ca and cb. The c 

pencil from A will appear to radiate 
from a in the same axis, likewise 
those from B as from 6, and the 
entire image will lie between a and 
6. The image is enlarged, because -"' 
the angle at which the lines from a 
and b enter the eye is greater than 
would be the lines proceeding di- 
rectly from A and B. Fig. 136. 

255. The visual angle is the 




EYE 



& 

Fig. 136. 

angle contained between two lines drawn from the center of 
the eye to the extremities of an object. (1) For the same 
object, the angle decreases with the distance of the object ; 
thus, if the same object, A B, is removed to A f B f , the visual 

^_A __— — — ^' 

EYE A 

JEj 




Fig. 137. 



angle decreases. Hence, if the size of an object is known, 
we may form some estimate of its distance by its visual 
angle, having learned by experience to associate together 



SPHERICAL MIRRORS. 



165 



distance and angular size. (2) For the same distance, the 
visual angle increases with the size of the object. Hence, 
if in any way the visual angle of a known object is in- 
creased, it appears magnified, and if decreased, the object 
appears smaller. The magnifying power of a concave mir- 
ror is dependent, not on the area of its surface, but upon 
its radius of curvature. 

256. In convex spherical mirrors the images are always 




' -^ EYE 



a %w> > fb 



1c 



erect, virtual, and smaller than 
the object. Thus, if A B be an 
object at any finite distance, the 
image of the point, A, will be 
somewhere on the axis, A C, and 
B on the axis, B C. The visual 
angle will be, in all cases, smaller 
than would the angle formed by 
the direct vision of the object 
A B. Fig. 138. 

Fig. 138. fe 

257. These laws are accurate when the mirror is a very 
small portion of a spherical surface. With a large portion, 
the reflected rays intersect each other, and their foci form 
curved lines, which are called caustics by reflection. Fig. 139. 

Thus the heart-shaped curve, formed 
by the reflection of a lighted candle 
from the concave surface of a tum- 
bler containing milk, is a caustic. 
Parabolic mirrors are used for the 
lanterns of locomotives, because, if 
a luminous point is placed in the 
focus of a concave parabolic mirror, 
all the rays which strike the mirror will be reflected exactly 
parallel. The light thus reflected maintains its intensity for 
a great distance. 




Fig. 139. 



166 



ELEMENTS OF PHYSICS. 



Recapitulation. 



Mirrors are either plane or curved. 



Curved mirrors are 



Spherical 



Conical 



f Convex. 
t Concave, 
f Paraboloid. 
I Ellipsoidal, etc. 



The Refraction of Light, or Dioptrics. 

258. When a pencil of light falls on a transparent 
body, (1) some of the rays are reflected, (2) some are 
absorbed, (3) some are transmitted. When a ray of light 
passes obliquely from one medium to another, it suffers a 
change in direction which is called refraction. 

259. The actual occurrence of this change in direction 
may be shown by placing a coin in an empty cup in such a 
position that it is just out of sight ; if, now, the cup be 
filled with water, the 
coin will become visi- 
ble, although neither 
the eye nor the coin 
has changed its posi- 
tion. Thus, if AB be 
the surface of the wa- 
ter, the ray, m E, pro- 
ceeding from the coin, 
appears to come to the eye in the line m' E. That is, it 
suffers a refraction when it passes from the water into the 
air. Its actual course is the bent line m I E. Fig. 140. 

260. Suppose an incident ray of light, Ac, (Fig. 141), 
moving in air, to meet the surface of water, R S, and let c E 
be the refracted ray. Draw PF perpendicular to the surface 




Fig. 140. 



REFRACTION. 



167 




Fig. 141. 



at the point of incidence, c ; then A c P is the angle of inci- 
dence, and EcF is the angle of refraction. It lies between 
the perpendicular and the refracted 
ray. If the incident ray falls more 
obliquely, as a c, the angle of re- 
fraction, ecf will become larger. 
In order to compare these angles, 
strike a circle with any convenient 
radius, as c R, and draw from the 
points, A 9 E, a, e y lines perpendicular 
to P F. These lines are called sines, and they are used to 
measure angles. A D and a d are sines of the angles of 
incidence ; E F and ef are sines of the angles of refraction. 
Now, it is found that A D -=- E F = ad -r-ef, or, in other 
words, the ratio which exists between the sines of the angles 
of incidence and of refraction is constant for the same two 
media. This ratio is called the index of refraction; that is, 

, . , „ ' J _. sine of the angle of incidence 

the index of retraction = ^— s ^ ^ — « — -. 

sine of the angle of refraction 

If light passes from air into water, the index of refraction 
is about | ; when light passes from water into air, the index 
of refraction is the reciprocal of this fraction, or f . 

261. The index of refraction varies with the media. 
The following table gives the indices of refraction when 
light passes from a vacuum into any of the substances 
named. 



Table of Absolute Indices of Refraction. 



Vacuum .... 1.0000 

Air 1.0003 

Alcohol . . . .1.374 
Crow r n-glass . . . 1.534 
Quartz Crystal . . 1.548 



Ice 1.309 

Water 1.336 

Bisulphide of Carbon 1.768 

Flint-glass . . . 1.830 

Diamond .... 2.439 



168 ELEMENTS OF PHYSICS. 

From this table we can readily find the relative indices 
for any two of the substances named, by dividing the abso- 
lute index of one by the other ; thus, when light passes 
from air into crown-glass, the index of refraction is irfMI? 
or about f ; from crown-glass into air it is f^ffr! > or i' 

In optics, the word dense signifies of great refractive 
power, and rare, of little refractive power — without reference 
to the specific gravity of the substance. The essential oils 
and alcohol are in this sense denser than water, although 
their specific gravity is less. 

262. When a ray of light passes perpendicularly from 
one medium to another, it is not refracted. If, in the ex- 
periment, on p. 166, the eye is directly above the coin, the 
coin is seen in its true direction, but there is also a curious 
effect produced of making the coin appear nearer than it 
really is. This is due to the fact that the rays which reach 
the eye from the edge of the coin are not perpendicular to 
the surface of the water, and hence suffer a refraction. 

When light passes obliquely from a rarer to a denser 
medium, it is refracted toward the perpendicular. When 
a star is near the horizon it appears to be higher than it 
really is, because, as its light passes through successive 
strata of the atmosphere, it is refracted more and more, and 
appears in the direction which the ray has when it enters 
the eye. 

When light passes obliquely from a denser to a rarer me- 
dium, it is refracted from the perpendicular. In this case 
the angle of refraction is always greater than the angle of 
incidence. 

Suppose light to pass from water into air. Fig. 142. As 
the angle of the incident rays IT I", etc., increases, the 
angle of the refracted ray, R R 1 R 2 , etc., also increases. 
There will be found some ray, as L, whose angle of refrac- 






REFRACTION. 



169 




Fig. 142. 



tion is a right angle, and the ray, if refracted, would coincide 
with the surface. If the incident 
angle is increased beyond this 
limit, say to TON, the ray can 
not suffer refraction, but will be 
totally reflected in the angle, NO T. 
This result may be shown by 
filling a goblet with water, and 
placing in it a spoon. When 
the eye is a little below the sur- 
face of the water, it will see a 
bright image of the part of the spoon immersed, reflected 
from the surface of the water. 

Refraction by Regular Surfaces. 

263. If a transparent body is entirely surrounded by air, 
a ray of light, on entering it, will be refracted toward the 
perpendicular, and, on emerging from the body, will be 
refracted from the perpendicular. 

(1) When the two surfaces of the medium are parallel, 
the incident and emergent rays are also parallel; because 
the ray is refracted an equal amount at each surface, and in 
the opposite direction. The two refractions do not cause 
any change in the general direction of the ray, but produce 
a slight lateral displacement, whose amount increases with 

the thickness of the medium 
and the obliquity of the in- 
cident ray. Fig. 143. 

A pane of glass occasions 
no distortion of the objects 
seen through it when its sides 
pig. 143. are perfectly parallel ; if they 

are not parallel, the objects will appear more or less dis- 
torted. 

Phys. 15. 




170 



ELEMENTS OF PHYSICS. 




Fig. 144. 



(2) A prism is a transparent medium having two plane 
surfaces not parallel. A prism may be a solid wedge of 
glass or crystal, or may consist of liquids inclosed in hollow 
prisms with sides of plane glass. The path of light through 
a prism is exhibited in Fig. 144. 
Suppose the light to come from 0. 
As the incident ray, D, enters 
the prism, it is refracted towards 
the perpendicular, P P 1 , because it 
enters a denser medium, and will 
proceed in the line D K. On leaving the prism for a rarer 
medium, it will be refracted from the perpendicular, P' P", 
and will emerge in the line K H. The light is thus twice 
refracted toward the base of the prism, and the eye which 
receives the emergent ray, K H, sees the object at 0' nearer 
the summit of the prism than the real position of the 
point, 0. 

(3) A lens is a transparent medium, having at least one 
curved surface. The curved surface is usually spherical. 

ABC D E F 




Fig. 145. 
There are six varieties of spherical lenses, viz. : A is a 
double convex, B a plano-convex, C is a meniscus, concave on 
one side and convex on the other, the convex surface hav- 
ing the shorter radius. These three are thickest at the 
center, and are converging lenses. D is a double concave, E is 
a plano-concave, and F is a concavo-convex, the concave sur- 
face having the shorter radius. These three are thinnest at 
the center, and are diverging lenses. Fig. 145. 



DOUBLE CONVEX LENSES. 



171 



The line, MN, which passes through a lens perpendicular 
to both surfaces, is called the axis of the lens. The double 
convex lens may be regarded as a series of prisms whose 
bases are turned toward the axis, and the double concave 
lens as a series of prisms whose bases are turned away 
from the axis. If the sides of each prism are infinitely 
small, the series will form a spherical surface. Hence, as a 
prism refracts light toward its base, a convex lens will re- 
fract the light tow T ard its axis, and tend to converge the 
rays ; a concave lens will refract light away from its axis, 
or tend to disperse the rays. We shall * study only the 
double convex and the double concave lenses, because the 
properties of these lenses are similar to the others of the 
same group. 

264. If parallel rays fall upon a convex lens, the rays 
will converge to one point, 
which is called the princi- — ^^ 
pal focus of the lens. This 
focus is real, for all the 

rays of the sun may be 

collected at this point. 
The ordinary burning- 
glass is simply a large double convex lens. Fig. 146. 

265. If the rays diverge from the principal focus they 
will be rendered parallel. A lamp so placed will illuminate 
objects at a great distance. Fig. 146. 




Fig. 146. 




Fig. 147 



266. If the rays diverge from a point beyond the prin- 



172 



ELEMENTS OF PHYSICS. 



cipal focus, as at I, they will converge on refraction to some 
point, as L, also at a greater distance than the principal 
focus ; and conversely if they diverge from L they will 
converge at I. Both these foci are real ; one is less than 
twice the principal focal distance and the other greater. 

267. Real images are formed when the object is at a 
finite distance beyond the principal focus. Suppose A B to 
be at more than twice the principal focal distance. A ray 
diverging from A will converge on refraction at a ; diverging 




Fig. 148. 
from B, at 6. Hence, the image of A B will be ab, real, 
inverted and smaller than its object. Conversely, if a b were a 
luminous object at less than twice the principal focal distance, 
but beyond the focus, its image would be A B, real, inverted, 
and larger than the object. 

If the rays diverge from a point nearer the lens than 




Fig. 149. 
the principal focal distance they will be less divergent on 
refraction, but will form no real focus, nor even be rendered 
parallel. Thus, the rays from L will appear to come from 
a virtual focus at I, which is on the same side of the lens as 



DOUBLE CONCAVE LENSES. 



173 



the luminous point. If a small object, as A B, (Fig. 150), 
were so placed, a virtual image would be formed at ab, 




Fig. 150. 

which would be erect, and larger than the object. This is 
the ordinary way of using a lens as a magnifying glass. 

268. The foci of concave lenses are always virtual, and 
the images formed by them are also virtual. Let A B be 

an object in front of a con- 



cave lens. The rays from 
the point, A, will be so re- 
fracted as to appear to come 
from its virtual focus, a, and 
the rays from the point, B, 
will appear to diverge from 
its focus, 6. Therefore, the 




Fig. 151. 



eye sees at a 6 an image of A B, which is always virtual, 
erect, and smaller than the object. 




Fig. 152. 

269. If a crystal of Iceland spar be placed upon an 
object, as in Fig. 152, a double image will be perceived. 



174 ELEMENTS OF PHYSICS. 

This phenomenon is called double refraction. Most transpar- 
ent bodies have the same property of refracting light in 
two separate pencils, but not to so great a degree. 

These doubly refracted rays have properties which dis- 
tinguish them from ordinary rays, and are said to be polar- 
ized. Light is also polarized by absorption, single refraction, 
and reflection. The subject of polarized light is so abstruse 
that it can not be taken up with profit in an elementary 
course. It must suffice us to say that when a ray has been 
polarized, it will neither be reflected, refracted, nor absorbed 
in precisely the same manner as common light, although the 
eye can not, unaided, distinguish one from the other. 

Recapitulation. 

I. Light is not refracted: 

1. In passing through a uniform medium, nor 

2. When passing perpendicularly from one medium to another. 

II. Light is refracted in passing obliquely into a second medium : 

1. Toward the perpendicular, when the second is the denser. 

2. From the perpendicular, when the second is the rarer. 

III. Lenses are either converging or diverging. 

IV. The effects of concave mirrors and of convex lenses are simi- 
lar: When the object is 

1. Nearer than the principal focal distance, 
The image is virtual, erect, and magnified. 

2. At the principal focus 

There is dispersion of light in parallel rays. 

3. Beyond the principal focus, but less than twice its distance, 
The image is real, inverted, and magnified. 

4. At twice the principal focal distance, 

The image is real, inverted, and of equal size. 



CAMERA OBSCURA. 



175 



5. At a finite distance, more than twice the principal focal 
distance, 

The image is real, inverted, and diminished. 

6. At an infinite distance, 

There is concentration of light at the principal focus. 

V. The effects of convex mirrors and of concave lenses are also- 
similar, forming images which are always virtual, erect, and smaller 
than the object. 



Optical Instruments, and Vision. 

270. If luminous rays are transmitted through a small 
aperture, and there received on a white screen, they form in- 




FlG. 153. 

verted images of external objects. The luminous rays pro- 
ceed in straight lines ; those from the top of the object, (Fig. 
153), are received on the bottom of the screen, and those 
from the base of the object on the top of the screen. The 
rays of light must, therefore, cross each other without inter- 
fering. A darkened room so arranged is one form of the 
camera obscura. 



176 ELEMENTS OF PHYSICS. 

The photographer's camera, Fig. 154, differs from this only 

A 




Fig. 154. 
in having a convex lens in the tube, A. The effect of the 
lens is to converge the rays so as to produce a small image 
of the object, which is, at the same time, clear and well 
defined. 

271. The mechanical action of the eye is very similar 
to that of the photographer's camera. The human eye is very 




Fig. 155. 

nearly spherical, and is about an inch in diameter. It con- 
sists essentially of (1) three enveloping coats and (2) three 
refracting bodies. Fig. 155 presents these parts in hori- 
zontal section. 



THE HUMAN EYE. 177 

(1) The outer coat, or white of the eye, is a tough and 
opaque membrane called the sclerotic. In the front part of 
this, the transparent cornea, a, is set in like a watch-glass. 

The middle coat, k, is the choroid, which consists of a 
membrane, abundantly supplied with blood-vessels, and cov- 
ered, on its inner face, by a dark, velvety substance, called 
the black pigment. 

The inner coat is the retina, m, which is mainly an expan- 
sion of the optic nerve, n, with the addition of terminal 
nerve elements for the perception of light, spread out in 
very fine net-work on the black pigment. 

Near the junction of the cornea and sclerotic, the choroid 
becomes thicker, and terminates in the ciliary processes. To 
the outer portion of these is attached an opaque, contractile 
membrane, d, called the iris, because it is the colored por- 
tion of the eye. The iris is pierced by an aperture, called 
the pupil, through which the luminous rays pass to the 
bottom of the eye. 

(2) Behind the iris, and supported by a suspensory liga- 
ment, attached to the ciliary muscle which proceeds from 
the ciliary processes, is the crystalline lens, /. This is a 
double convex lens, having its anterior face of less con- 
vexity than the posterior. 

The portion of the eye, e, between the cornea and the 
crystalline, is filled with a thin liquid, called the aqueous 
humor. 

Behind the crystalline is the chamber, h, which is filled 
with a jelly-like liquid, called the vitreous humor. The 
humors and the crystalline are each surrounded by a deli- 
cate membrane, or capsule. 

If a luminous point be placed before the eye, the central 
rays pass through the cornea and enter the aqueous humor. 
Of these rays, the more divergent are cut off by the iris, 



178 ELEMENTS OF PHYSICS. 

and only those that are nearly parallel are admitted through 
the pupil. These are transmitted through the crystalline 
and the vitreous humor, and finally fall upon the retina. 
The effect of these refracting bodies is to form at, or 
very near, the retina an image of the luminous point. 
The same being true of all diverging pencils proceeding 
from an object, there will be formed on the retina a small 
inverted image of the object. 

272. The sensation of sight is due to the impression 
made by the image on the terminal percipient nerve ele- 
ments of the retina, and thence conveyed by the optic nerve 
fibers to the brain. These nerve elements are contained in 
a layer next the black pigment, and consist of a great num- 
ber of very minute bodies, arranged side by side, and re- 
sembling rods and cones, standing perpendicularly to the 
surface of the retina. It is supposed that the waves of 
light falling upon this layer of rods and cones produce vibra- 
tions, which are conducted by the nerve fibers in such a way 
to the brain that it is excited and acknowledges the recep- 
tion of the luminous image on the retina. 

273. The impression made on the retina is not instan- 
taneous, and when once made continues, on th'e average, for 
nearly one-third of a second after the exciting cause has 
ceased to act. If, therefore, an ignited coal be whirled 
about rapidly, luminous rings are produced. 

Many optical toys owe their 
effect to the duration of the 
impression on the retina. The 
Thaumatrope, Fig. 156, con- 
sists of a card which is made 
to revolve by means of strings g. 156. 

attached to its sides. A horse may be so painted on one 




VISION. 179 

side and a rider on the other, that a rapid revolution of the 
card will cause the rider to appear seated on the horse. 

274. The accommodation of the eye to different dis- 
tances is effected by the action of the ciliary muscle upon 
the crystalline lens. When the eye is turned toward a dis- 
tant object, the muscle relaxes and the lens is flattened ; but, 
for near objects, the muscle contracts and the lens becomes 
more convex. In this way the conjugate focus of the object 
is made always to fall upon the retina. The power of ac- 
commodation is very great, and is exerted unconsciously 
with marvelous rapidity. Nevertheless, there is, for all eyes, 
a certain distance at which the parts of an object, as the 
letters on this page, are seen most distinctly. This distance, 
which, for ordinary eyes, varies from five to ten inches, is 
called the distance of distinct vision. 

275. Far-sighted eyes are those whose nearest point of 
distinct vision exceeds ten inches, and near-sighted eyes are 
those whose farthest point of distinct vision is a short dis- 
tance, varying from three inches to twenty feet. For normal 
eyes, the farthest point of distinct vision is infinitely distant, 
the nearest point more than three inches. 

276. An object will not appear distinct to the normal 
eye unless the rays which proceed from it enter the eye 
nearly parallel. This will be the case for a luminous point 
when it is distant more than eighteen inches. If a printed 
page be brought too close to the eye, the letters appear more 
or less blurred, because the rays are too divergent to focus 
on the retina. Now, place between the eye and the page a 
thin card in which a pin-hole has been pricked. The card 
will exclude the outer divergent rays, and the eye will be 
able to converge the few nearly parallel rays which pass 
through the pin-hole upon the retina, and thereby form a 



180 



ELEMENTS OF PHYSICS. 



faint, but distinct, image. At the same time, the letters will 
appear magnified, because the visual angle is increased. 

277. A convex lens placed a little nearer an object than 
its focal distance will converge all its rays upon the retina, 
thus preserving all the light while it magnifies the object 
by increasing its visual angle. With a powerful lens the 
object must be very near the lens, and, consequently, the 
field of view will be very small. The magnifying glasses used 
for viewing pictures magnify but little, because their radius 
of curvature is very large, but they afford a large field of 
view. Pocket microscopes usually contain two or three convex 
lenses, acting as a single thick lens. They seldom magi/" 
more than five diameters. 

278. The compound microscope consists of an obje 
glass, M, of short focus, and an eye-glass, N, of less mag: 
fying power. The object, A B, is placed a little beyond t 




Fig. 157. 

focus of the object-glass, and its reai image, a b, inverted an* 
magnified, is formed a little within the focus of the eye-glass 
By this glass the real image is viewed as with a simph 
microscope, and, hence, forms another image, a'b r , which u 
still more magnified, and is virtual. The advantage of this 
form of microscope is that a high magnifying power is ob- 
tained with a comparatively large field of view. 

The difference between the simple and compound micro- 
scopes consists in this, that in the simple microscope the 
object is viewed directly, and in the compound microscope a 
real magnified image of the object is viewed with a common 
magnifier. 



THE TELESCOPE. 



181 



279. The telescope is used for viewing distant objects. 
In refracting telescopes a real image is formed by an object- 
glass of small convexity ; in reflecting telescopes a real 
image is formed by a concave mirror ; these images are, in 
both cases, very small, but very bright. They are then 
viewed by an eye-glass of high magnifying power. 

280. The astronomical refracting telescope consists 
of the object-glass, M y and the eye-glass, N. Fig. 158. The 
object-glass forms an inverted image, 6 a, of a distant object, 



i 




Fig. 158. 



iB, in its principal focus, F. This image is then viewed 
I the eye-glass, iV, w T hich is so placed as to receive the 
lage at a distance a little less than its own focal length. 
he image is inverted. This occasions little inconvenience 
i viewing heavenly bodies, but would be a serious defect 
[ employed for terrestrial objects. 

281. The terrestrial telescope has, therefore, two addi- 
lonal lenses for rendering the image erect. Fig. 159. The 




Fig. 159. 



'action of these glasses, P and Q, will be understood by 
tracing the rays from the luminous point, A. P renders them 
parallel, and gives them a new direction. Q converges them 
in the focus of the eye-glass, so as to form a real image 
which has the same position as the object. This second 



182 



ELEMENTS OF PHYSICS. 



image is then viewed in the ordinary way by the eye-glass, 
R. 

282. Reflecting telescopes have several different forms. 
Herschel's telescope is represented in Fig. 160. It consists 




Fig. 160. 

of a concave reflector, M, and a convex lens/ 0. The 
reflector is so inclined to the axis of the tube that the 
image of the star is formed near the side of the tube, in 
front of the eye-piece, 0, and is then magnified by the lens 
and received by the eye. 

Lord Rosse's telescope has a mirror six feet in diameter. 
The amount of available light received at the eye-piece 
exceeds 250,000 times as much light as commonly enters 
the eye. This enormous illuminating power enables the 
observer to use eye-glasses whose magnifying power is 6,000 
diameters. This would render an object as large as the 
capitol at Washington visible at the distance of the moon. 

Alvan Clarke, of Boston, has lately succeeded in making a 
refracting telescope for the Washington observatory, whose 
object-glass is 26 inches in diameter. 

283. The magic lantern is an instrument by which 
translucent objects are magnified and thrown on a screen. 
Fig. 161. A lamp is placed in the common focus of a 
reflector, MN, and of a convex lens, J., so that a strong 
beam of light is thrown on the object which is inserted in 



THE STEREOSCOPE. 



183 



the slit, CD. A magnifying lens at B forms an image of 
the object on the screen, EF. The objects are usually painted 
on glass, but the instrument may also be used to magnify 
any translucent object. 




fig. 161. 

The solar microscope is essentially a magic lantern illumi- 
nated by the sun. 

284. The stereoscope. If a solid object, as a die, be 
held a short distance before the eyes, each eye will see the 
object from a different point of view ; and, consequently, 




/• 


J 


• 


• 'I 




\ 


• 


J 



Fig. 162. 

the two images formed on the retina will not be exactly 
alike. Fig. 162 represents a die as seen by the left and 
right eyes respectively. By the blending of these tw T o 
images, the object appears solid. This effect will be pro- 
duced in the engraving, if a card be held between the two 
figures, and they are steadily looked at for a few seconds, 
one by the right eye and the other by the left. The stereo- 
scope, Fig. 163, is contrived to assist the eye in blending 
two slightly different pictures of the same object, taken 



184 



ELEMENTS OF PHYSICS. 



from points of view related to each other in the same man- 
ner as the two eyes of the observer. These pictures are 
placed in the bottom of a box and viewed // .. 

through two eye-pieces, which are segments O jy O 

cut from a double convex lens. A dia- 
phragm, D, (Fig. 164), prevents each eye — > ^ v ^ 




c 

Fig. 163. Fig. 164. 

from seeing more than one picture. The rays of light from 
A after emerging from the lens, M y reach the eye as if they 
came from C, and the rays from the lens, N, also appear to 
come from C. Thus, the two pictures are blended in one, 
and appear to come from a solid object at C. 



I. The human eye 
consists of 



Recapitulation. 

Enveloping 
coats. 

Refracting 
bodies. 



Sclerotic. 
Choroid. 
Retina. 

Aqueous humor 
Crystalline lens. 
Vitreous humor. 



II. The sensation of sight is produced by luminous vibrations 
passing through the cornea, aqueous humor, pupil, crystalline lens, 
vitreous humor to the retina, and there exciting, in the layer of 
rods and cones, vibrations which are conveyed by the optic nerve 
fibers to the brain. 

III. All optical instruments are combinations of either prisms, 
lenses, or mirrors. 






CHROMATICS. 

IV. Microscopes are used for magnifying near objects. 
Telescopes are used for magnifying distant objects. 

V. Microscopes are simple, and compound. 
Telescopes are refracting, and reflecting. 



185 



Chromatics, or Colors. 

285. If a pencil of solar light be admitted into a 
darkened room through a very small aperture, it will form 
a round, white image of the sun, as represented at K, (Fig. 
165). If, now, a prism be placed in the path of the pencil, 
it will form on a screen an elongated band of colors, which 




N ljg^ZlS 



Fig. 165. 
is called the solar spectrum. That is, the prism not merely 
refracts the rays, but refracts them unequally, and produces 
what is called the dispersion of light. Newton distinguished 
seven of these colors as primary, which are, beginning with 
the least refracted, red, orange, yelloiv, green, blue, indigo, 
violet. 

286. White solar light is, therefore, composed of differ- 
ent colored rays. An additional proof of this is found in the 

Phys. 16. 



186 



ELEMENTS OF PHYSICS. 



fact that, when all the colors of the spectrum are recom- 
bined, they will reproduce white light. Thus, if all the 




Fig. 166. 

rays of the spectrum are received on a convex lens or on a 
concave mirror, a white image will be formed in the focus. 
If a circular card be painted with the seven colors and 
revolved rapidly, it will appear of a white color, more or 
less pure according as the colors on the card more or less 
exactly imitate those of the spectrum. Fig. 166. 

287. If the solar light be admitted through a very 

££f* 




Fig. 167. 



narrow slit and received on a good flint-glass prism, it will 



FRAUNHOFER'S LINES. 187 

be found that the colors of the spectrum are not continuous, 
but that they are interrupted by numerous dark spaces, 
known as Fraunhofer's lines. On viewing the spectrum 
with a telescope two thousand of these lines are visible. 
Seven are more distinct than the rest, and are designated 
by the letters B, C, D, E> F, G, H> to serve as means of 
reference. Fig. 167. 

288. The index of refraction for the different colors is 
fixed w T ith precision by ascertaining the position of Fraun- 
hofer's lines, B, C, etc. The table on p. 167 gives the index 
of refraction for the line E in the yellowish -green rays, 
which is assumed as the mean of all the rays. If similar 
prisms are made of different substances the mean refraction 
may be very nearly the same, and yet the spectra they fur- 
nish be of very unequal lengths. The dispersive power of a 
medium indicates the amount of separation it produces in 
the extreme rays compared with the amount of refraction 
in the mean rays. 

Table of Dispersive Poivers. 

Bisulphide of Carbon 0.130 Crown-glass . . . 0.036 
Flint-glass . . . . 0.052 Water .... 0.035 
Diamond .... 0.038 Quartz crystal . . 0.026 

289. If two prisms, exactly alike, are placed near each 
other, with their bases turned in a 

contrary direction, the one will ex- 
actly neutralize the other, and the 
light will emerge from the second as 
if from a medium with parallel faces. 

Now, suppose two unequal prisms, one ~ ~" ~* 

Fig. 168. 
of flint and the other of crown-glass, 

be placed together, as in Fig. 168. The dispersive power 

of flint-glass is almost double that of crown-glass, while 





188 ELEMENTS OF PHYSICS. 

its refractive power is but little greater ; hence, if the refract- 
ing angle of the former is made so much smaller than the 
latter that their dispersive powers are equal, only white 
light will emerge, but it will be refracted with about half 
the refracting power of a single prism of crown-glass. 

An achromatic lens is made on the same principle by 
combining a double convex lens of crown-glass 
with a concavo-convex lens of flint-glass. Fig. 
169. Such a lens transmits uncolored light. In 
any single lens, the image is fringed with colored 
rays, which are due to the dispersive power of 
the lens. Fi<Ti69. 

290. The spectra formed by artificial lights are usually 
wanting in several colors, but yield the remainder with the 
same refrangibility as the corresponding colors of the solar 
spectrum. An almost colorless flame may be produced 
by burning pure alcohol, or by burning gas in a Bunsen's 
burner. If a platinum wire be dipped in common salt, or in 
any sodium compound, and held in a colorless flame, the 
sodium will vaporize and emit a very pure yellow light. 
Lithium yields a pure red. Several other substances yield 
characteristic colored flames: thus, strontium gives a red 
color ; potassium, purple ; copper, green. 

291. The spectroscope is an instrument used for analyz- 
ing flames. Fig. 170. The substance which colors the 
flame is placed on platinum wires in a Bunsen's burner at 
E, and vaporized. The light which it emits is received 
through a narrow slit in the end of the tube, J., where it is 
condensed by lenses and thrown on the prism, P. The 
refracted rays fall on the object-glass of a small telescope, B, 
and pass through it to the eye. The tube, C, is not neces- 
sary, but is added for the sake of convenience. It contains 
a transparent scale which is divided into equal parts. When 



THE SPECTROSCOPE. 



189 



a candle is placed in front of C, it casts a bright image of 
the scale on the prism, which is reflected into the tube, B, 




Fig. 170. 

so that the observer sees at once the refracted rays and the 
lines of the scale to which they correspond. 

Sodium gives a bright line, identical in refrangibility with 
the dark line, D, in the solar spectrum. Thallium gives a 
green line near the dark line, E. The light emitted by 
these substances is monochromatic ; that is, of only one color. 
Potassium gives a red line near A, and a violet ray near H. 
Strontium gives several red lines between B and D, and a 
blue line between F and G. The light emitted by these 
substances is, therefore, not homogeneous, but contains two 
colors. Any substance which can be volatilized will furnish 
a spectrum of a few bright lines which have a constant 
degree of refrangibility. This is also true of incandescent 



190 ELEMENTS OF PHYSICS. 

gases : hydrogen yields three bright lines, which are iden- 
tical in position with C, F, G. If several substances are 
mixed, each will give its own system of lines as if it were 
burned separately. This property has been turned to 
account in chemistry in detecting the presence of sub- 
stances that are easily volatilized. For these bodies, it is an 
exceedingly sensitive test. It is, in fact, difficult to obtain 
a flame that does not show the presence of sodium, as 
T8 o oWo"o o" °f a g ram of sodium will yield its yellow line. 
Since the year 1860 four new metals have been discovered 
by the aid of the spectroscope. Two of these, caesium and 
rubidium, are widely distributed, being found in many min- 
eral waters, and in the ashes of tobacco, but in such small 
quantities that the usual chemical tests failed to detect 
them. 

292. If light, which would give a continuous spectrum, 
is passed through certain almost transparent and colorless 
solutions and then examined, dark lines are found, which 
are owing to the fact that the solution has absorbed some 
of the rays. Thus, solutions of didymium give two dark 
lines, one in the yellow and the other in the green. The 
gases also produce absorption bands; the vapors of iodine 
and bromine produce remarkable series of black bands. 
Even the atmosphere exerts an absorptive power, which is 
especially energetic when the sun is near the horizon. 
Some of Fraunhofer's lines are, undoubtedly, due to the 
air, but the larger portion must have another cause. 

293. If two sodium flames are placed before the spec- 
troscope, so that one must pass through the other, no 
spectrum is produced. In other words, sodium vapor 
absorbs the same rays that it emits. So, also, if the 
lime-light which gives a continuous spectrum is passed 



SPECTR UM ANAL YSIS. 191 

through a sodium flame, a dark line is found in the place 
where the yellow sodium ray should be, and the spectrum 
is said to be reversed. These phenomena are exhibited by 
so many substances that we may group the effects produced 
in two general statements. 

(1) Every substance, when rendered luminous, gives out rays 
of a definite degree of refrangibility. 

(2) Every substance has the power of absorbing the same kind 
of rays that it emits. 

294. In view of these facts, Kirchhoff supposes (1) 
that the nucleus of the sun emits a continuous spectrum, 
containing rays of all degrees of refrangibility; (2) that the 
luminous atmosphere of the sun contains vapors of various 
elements, each of which would, by itself, give its system of 
bright lines ; (3) that when the light from the nucleus is 
transmitted through this luminous atmosphere, the bright 
lines that would have been produced by the atmosphere are 
reversed ; and (4) that Fraunhofer's lines are these reversed 
lines. 

Since the bright lines of the elements coincide with very 
many of Fraunhofer's lines, it is fair to suppose that these 
elements exist in the sun. Iron gives four hundred bright 
lines which coincide with Fraunhofer's lines. Eighteen dif- 
ferent metals give similar coincidences. Hence, we are led 
to suppose that the sun contains iron, manganese, nickel, 
calcium, copper, sodium, hydrogen, and some other ele- 
ments. Hitherto no evidence has been given of the 
presence of gold, silver, mercury, and many other elements. 

The fixed stars also show similar coincidences ; thus Sirius 
and Aldebaran are thought to contain sodium, magnesium, 
and hydrogen. The comets and nebulse give spectra with 
bright lines, which seem to show that these bodies are 
incandescent gases. 



192 ELEMENTS OF PHYSICS. 

295. When a sunbeam falls on a film of oil floating on 
water, or on a soap-bubble, we notice a very brilliant dis- 
play of colors. The light is reflected to our eyes both from 
the outer and inner surface of the film, and produces the 
phenomena of interference and combination. This is a con- 
firmation of the wave theory of light. We may obtain 
similar phenomena in various ways. One of the simplest 
methods is the following : Press together a convex lens, A B, 
of long radius of curvature, upon 
a plate of plane glass, D E. If a Al K ^f^^^ ^ 




beam of monochromatic light falls ^ i"»»~ _ r _. 
perpendicularly on the lens, a F ^. 171. 

portion of it will be reflected from the convex surface, 
ACB, and another portion from the plane surface, D E. 
These two systems of waves will intersect in 
crests and hollows according as their paths 
differ by an even number of semi-undulations, 
or by an odd number. At a certain distance 
fig. 172. from C, as at F, the two waves will meet in 
opposite phases and destroy each other, and, hence there 
will be a black ring at F. At a greater distance, as at G, 
the waves will meet in the same phase and increase the 
amplitude of vibrations, and there will be a bright ring of 
the same color as the light. Other points will be found 
beyond G, in which the waves will meet in opposite or in sim- 
ilar phases, and, consequently, a series of black and colored 
rings will be found about the center, C. 

If the solar light be employed, each ring contains all the 
colors of the spectrum, because the colors have different 
refrangibilities, and the rings are not exactly superimposed. 

296. These rings are known as Newton's rings. Now, 
as we can calculate exactly the distance between the two 
surfaces, we have a means of determining the wave length 



COLOR OF LIGHT. 



193 



due to various colors. The following table has been con- 
structed in accordance with these data : 



Colors. 


Lengths of waves 

in parts 

of an inch. 


Number 

of waves in an 

inch. 


Number 

of waves in a 

second. 


Extreme red . . . 
Red 


.0000266 
.0000256 
.0000240 
.0000227 
.0000211 
.0000196 
.0000185 
.0000174 
.0000167 


37640 
39180 
41610 
44000 
47460 
51110 
54070 
57490 
59750 


442000000000000 
458000000000000 


Orange 

Yellow 

Green 


489000000000000 
517000000000000 
558000000000000 


Blue 


599000000000000 


Indigo 


634000000000000 


Violet •. 


675000000000000 


Extreme violet . 


702000000000000 



297. The color of light is determined by the frequency 
of its vibration, or by the length of its wave. Light and 
sound are somewhat similar. We found that the low tones 
have a slow rate of vibration and a great wave length. So 
the luminous rays that are the least refracted are longer and 
slower than those that are more refracted. But the student 
will not fail to notice how very small and how very rapid 
are light waves when compared w 7 ith sound waves. 

298. It is usual to classify the properties of the spec- 
trum in three groups : Luminous, Heating, and Chemical. 
Every ray possesses, it is probable, all of these properties, 
but not in equal intensity. Thus the maximum chemical 
effect is found in the rays of high refrangibility ; the maxi- 
mum heating effect in the rays of low refrangibility ; the 
maximum luminous effect in the rays of nearly mean refran- 
gibility, viz. : the yellow. The curves in Fig. 167, show 
the relative intensity of each property in a spectrum pro- 
duced by flint-glass. It will be noticed that the spectrum 

Phys. 17. 



194 ELEMENTS OF PHYSICS. 

is drawn as if extending beyond the colored rays ; that is 
to say, there are heat rays that the eye can not perceive 
because their rate of vibration is too slow, and there are 
chemical rays which it can not perceive because their rate 
of vibration is too great. These invisible rays do not differ 
in kind from the visible rays. 

Some persons are color-blind, and can not distinguish 
colors at all, although in every other respect their sight is 
perfect. The most common defect of this sort is an in- 
ability to distinguish red colors. A person "red-blind" 
believes that ripe cherries are of the same color as the 
leaves which hang near them. 

299. The natural color of a body is due to the power 
it has of extinguishing certain vibrations, and of reflecting 
or transmitting others. A red cloth reflects the red rays and 
absorbs the rest ; red glass transmits only the red rays. A 
body that reflects all the rays of the solar spectrum is 
white ; a body that reflects but very little light is black. 

A curious experiment illustrates that the color of a body 
is not inherent. Darken a room, and then set on fire a cup 
of alcohol which has been saturated with common salt: 
every object will be illuminated by the yellow light of 
sodium, and appear of a yellow color. As this light falls 
on the faces of those near the cup, it gives them a ghastly 
appearance, which is quite wonderful to those who see the 
effect for the first time. 

Recapitulation. 

When solar light is examined with a prism, it is found to consist 
of seven primary colors, which are interrupted by dark lines. 

Other luminous bodies yield spectra which resemble the solar 
spectrum in many particulars. 

All spectra have luminous, thermal, and chemical properties, but 
not in equal intensity. 



COLORS. 195 

The spectrum analysis depends on the fact that every luminous 
body emits rays of definite refrangibility. 

The dark lines are explained by the fact that every luminous body 
is capable of absorbing the rays which it emits. 

Luminous vibrations may be made to combine and interfere by 
reflection and refraction. 

Colors are dependent on the frequency of the luminous vibrations. 

Problems. 

1. It is calculated that the light from the polar star requires 3 h 
years to reach the earth ; what is its distance ? 

2. What are the relative intensities of two lights that cast equal 
shadows at distances from an opaque rod respectively 6 inches and 
6 feet? 

3. A wax candle is fixed at 10 inches from the opaque rod; what 
must be the distance of a gas-light from the same rod to cast an 
equal shadow when the gas burns with "12 candle power?" 

4. What will be the index of refraction when light passes from 
crown-glass into bisulphide of carbon? When it passes in the 
other direction? 

5. What will be the relative lengths of two solar spectra produced 
under the same circumstances by prisms of quartz and of bisulphide 
of carbon? 

6. With red taken as unity, find the ratio between the relative 
number of vibrations in the colors of the spectrum, and compare 
with the relative number of sonorus waves in an octave. Will the 
comparison warrant any analogy between vibrations of light and of 
sound ? 



CHAPTEK XV. 

THE PHENOMENA OF HEAT, OR PYRONOMICS. 

300. The phenomena of heat are so generally manifest 
that we have had frequent occasion to refer to them, and 
have explained the methods by which heat may be meas- 
ured. It may be noticed that our sensations of warmth and 
cold are only relative, and are sometimes utterly untrust- 
worthy as a means of measuring heat. If we place the 
right nand in iced water and the left in hot, and then 
transfer both to ordinary cistern water, the left hand will 
pronounce the cistern water cold and the right hand" pro- 
nounce it warm. So, also, if we pass from the outer air of 
a winter's day into a heated room, our sensations may lead 
us to declare it overheated, even while the occupants of the 
room are somewhat chilly. 

We have also noticed that one effect of heat is to render 
bodies incandescent, and that the solar rays have their maxi- 
mum heating effect near the red rays. These phenomena, 
as well as others that we shall have occasion to study, so 
connect heat with light that we are almost justified in assum- 
ing that their phenomena are due to the same force. Both are 
certainly forms of energy by which molecules of matter are 
thrown into vibrations and give rise to waves of crests and 
hollows. They differ in the fact, that the eye recognizes as 
light only those waves which have certain limits of rapidity 
of motion, and which are, at best, very small, while waves 
of heat can be recognized that are, in comparison, large and 
of slow rate of motion ; although it is not meant to be 
(196) 



EFFECT OF HEAT. 



197 



stated by this that heat waves may not also accompany, or 
be identical with, the most refrangible luminous waves. 

Besides these phenomena, heat produces certain effects 
within the bodies upon which it acts, which we shall now 
proceed to consider. 

301. The first effect of heat on any body, solid, liquid, 

or aeriform, that is not destroyed by it, is to expand it. 

The expansion of gases may be shown by the air- ther- 
mometer. Fig. 173. This consists of a bulb of glass with 

a long stem, which dips into a colored fluid. 

If the bulb be warmed by the hand, the 

air inclosed will so expand that a portion 

will be expelled and rise in bubbles through 

the fluid. On cooling, that portion of the 

air which remains will contract to its former 

volume, and the fluid will rise to take the 

place of the air expelled. 

On repeating this experiment with other 

gases, it will be found that all aeriform 

bodies expand equally and regularly for equal 

successive increments of temperature. The ex- 
pansion is ^y for each degree F., or ^y^ 

for each degree C. 

The expansion of liquids may be shown by a flask 
having a long narrow tube fitted to its neck by a cork. 
Fig. 174. If the flask be filled with alcohol and 
plunged in boiling water, the expansion of the 
alcohol will be shown by its rise in the tube. Coal 
oil expands more than alcohol, but most other 
liquids less, showing that different liquids expand 
unequally for the same increments of temperature. 
More accurate experiments show that each liquid 

also expands irregularly. On being raised from 32° F. to 




Fig. 173. 




Fig. 174. 



198 



ELEMENTS OF PHYSICS. 



212° F. alcohol expands -^ of its volume, water about ^ T , 
and mercury ^\. 

The expansion of solids may be illustrated by the ap- 
paratus given in Fig. 5. These experiments show an 
increase in volume which is termed cubical expansion. In 
solids the expansion is sometimes measured in one direction 
only, and is then termed linear expansion. 

Fig. 175 represents the pyrometer, an instrument which 
shows the linear expansion of solids, and which is sometimes 




Fig. 175. 

used to measure very high temperatures. A metallic rod, 
J., fixed at one end, jB, presses at the other end the short 
arm of the index, K. When the rod is heated it expands 
and drives the index along the scale. 

302. Different solids expand unequally for equal in- 
crements of temperature. If two thin bars of iron and 
brass are riveted together at different points along their 
whole length, and boiling water is poured on them, it will 



Fig. 176. 



Fig. 17 



bend so that the brass will be on the convex side of the 
curve. If it is then plunged in cold water, it will curve in 
the opposite direction. The reason of this is, that the brass 
expands and contracts more than the iron, and the bar 
curves, so that the longest bar shall be on the convex side. 



EXPANSION. 199 



Table of Expansion from 32° F. to 212° F. 



Liuear. Cubical. 



Flint-glass . ^g tit Bras s - . . ■ . zfa ih 

Platinum . . jfa ^ Silver . . . . -^ 

Steel .... -9^-g -j-^-g- Tin --J-g- -pf-j 

Iron .... -A* ^ Zinc . . . . A 



i 

T71 



i 



8T6* 2"g~2 ^ 111C .... -j-jtj- fTJ 



The fractions in the above table of linear expansion show 
what proportion of its length a body will increase in being 
raised from 32° F. to 212° F. It will be noticed that the 
cubical expansion is expressed by a fraction three times as 
large. With very few exceptions, all bodies contract on 
cooling to their original dimensions. 

303. When water is heated from 32° F. to 212° F. it 
expands .0466 of its volume ; it is compressed by a pressure 
of one atmosphere .000044 of its volume. Therefore, it would 
require a pressure of over 1000 atmospheres to restore boil- 
ing water to its bulk when at the freezing point, or to pre- 
vent its expansion on being heated 180°. We see from this 
that the amount of force exerted in expansion or contrac- 
tion by heat is enormous. The expansive force of water for 
each degree F. is nearly 1 1 ^/ ) = 6 atmospheres, or 90 pounds 
per square inch. 

A bar of wrought iron expands for each degree F. with a 
force of nearly two hundred pounds per square inch. Hence, 
it is often necessary to take into account the changes in 
length which are produced by variations in temperature. 
Iron beams built into masonry should be left free at one 
end. 

We have an application of the same principle in the 
method by which tires are secured on wheels. The tire, 
made a little smaller than the wheel, is heated red-hot, and, 



200 ELEMENTS OF PHYSICS. 

while expanded, placed in position. On cooling, it not only 
secures itself on the rim, but holds all the other parts of 
the wheel in position. 

Brittle substances, as glass or cast-iron, often crack when 
heated suddenly ; because the outside is heated sooner than 
the inside, and thereby causes an unequal expansion. The 
thicker the plate, the greater the liability to fracture. A 
sudden cooling by producing an unequal contraction, has the 
same tendency to fracture. 

304. Water presents an exception to the general law of 
expansion and contraction by heat. If a flask with a long 
and very slender neck, Fig. 174, be filled with boiling water 
and allowed to cool, the water will contract until it reaches 
the temperature of 39°. 2 F. It then begins to expand, 
and continues to do so until it freezes. At 32° F. it occu- 
pies the same space that it did at 48° F. The maximum 
density of water is, therefore, attained at 39°. 2 F., and above 
or below this temperature it expands. 

This fact is of infinite importance in nature. In winter, 
the lakes and rivers cool until they attain their maximum 
density throughout. If the cooling proceeds further, expan- 
sion begins at the surface, and the lighter, though colder, 
particles float on the warmer particles below. Hence, the 
freezing takes place only at the surface. 

At the moment of freezing, water, in becoming solid ice, 
undergoes a sudden increase of about ten per cent in 
volume. The ice, once formed, covers the water like a 
blanket, and renders the freezing process very slow. If the 
ice had a greater specific gravity than water, it would sink 
to the bottom, and in time our lakes would become solid. 

305. The second effect of heat on a solid is to melt it. 
Some solids, as paper, wood, wool, do not melt, but are de- 
composed. The temperature at which any solid melts is 



. —37.9 


Bismuth . . 


. 512. 


• + 9.5 


Lead .... 


. 620. 


. . 32. 


Zinc .... 


. 680. 


. . 111.5 


Silver 


. 1832. 


. . 136. 


Gold .... 


. 2282. 


. . 451. 


Wrought Iron . 


. 2912. 



FUSION. 201 

invariable for the same substance, if the pressure is the 
same. This temperature is called the melting point. 

Table of Melting Points, in Degrees Fahrenheit. 

Mercury . . 

Bromine 

Ice .... 

Phosphorus 
Potassium 
Tin ... 

Certain bodies, as iron, platinum, glass, and wax, soften 
before they fuse and become plastic. It is in this plastic 
state that glass is worked and iron or platinum forged. 
The melting point of alloys is often lower than that of 
either of its components. Rose's metal, which consists of 
four parts of bismuth, one of lead, and one of tin, fuses at 
201° F. 

306. If a liquid is cooled sufficiently it generally 
solidifies at the melting point, but the freezing point may 
be lowered by various means. 

If water is boiled to expel the air and then allowed to 
cool very slowly and without agitation, it sometimes reaches 
10° F. before it freezes. When in this condition, any dis- 
turbance, as a jolt or the addition of a bit of ice, will cause 
immediate congelation throughout the entire mass. The 
temperature will rise to 32° F. In fine capillary tubes, 
water has been lowered to — 4° F. without solidifying. This 
probably explains why sap is not frozen in plants. 

The presence of salts in solution lowers the freezing point 
of water. Saturated brine freezes at — 4° F. Sea-water 
freezes at 27°. 4 F. In such cases, nearly pure ice is formed. 
The water appears to crystallize out, leaving the salt behind. 
Weak alcoholic mixtures, like wine and cider, may be con- 



202 ELEMENTS OF PHYSICS. 

centrated by exposing them to cold and removing the layers 
of ice as they form. 

307. Water expands with enormous force at the mo- 
ment of freezing. Bomb-shells an inch thick, filled with 
water, have been burst by the freezing of the water. On a 
smaller scale, the fact is familiar to northern housekeep- 
ers in the breaking of utensils in which water has been 
allowed to freeze. Cast-iron, bismuth, antimony, and type- 
metal also expand on solidifying. These substances give 
sharp casts, because, when the metal sets, the expansion 
forces it into the minute lines of the mold. Most sub- 
stances contract on solidifying. Coins of copper, silver, and 
gold are not cast, but stamped. 

308. The third effect of heat is vaporization. Some 
solids, as iodine, arsenic, and camphor, vaporize without 
becoming liquids ; but, generally, vapors are formed from 
liquids, as liquids are from solids. If the vaporization takes 
place quietly, it is termed evaporation; but, if the liquid is 
agitated by the formation of bubbles of its own vapor, the 
process is termed boiling. 

309. The evaporation of water is going on constantly 
in nature, and is one of the means by which the earth is 
rendered fit for the maintenance of life. The principal cir- 
cumstances which influence the evaporation of water are the 
following : 

(1) The temperature. Evaporation may go on at very low 
temperatures. Snow and ice disappear from the ground 
even when there has been no thawing. Clothes are dried 
on a winter's day when the thermometer shows a tempera- 
ture below freezing. Increase of temperature favors evap- 
oration. In summer, the roads are soon dry after a shower, 
"because the evaporation is rapid. 



EVAPORATION. 203 

(2) The amount of surface exposed; because evaporation 
proceeds only from the surface. 

(3) The condition of the air. The air can hold only a 
limited amount of aqueous vapor. At 32° F. one cubic 
foot of air can hold only 2.37 grains of aqueous vapor, which 
is 2-g-g- part of its weight. For every increase of 20° F. the 
capacity of air for moisture is nearly doubled ; at 52° F. it 
can absorb j\^ part of its weight ; at 72° F. about ■£§ part, 
and so on. When air contains as much moisture as it can 
hold, it is said to be saturated, and evaporation must cease. 
Therefore, evaporation is most rapid in dry air. 

Now, if the air above a liquid is not changed, it becomes 
saturated. Hence, evaporation is more rapid in a breeze 
than in still air. For this reason a warm, sultry day is less 
favorable to evaporation than a cold day with a brisk wind. 

310. Suppose air at 72° P. to be saturated with moist- 
ure, and then to cool gradually. As the temperature low- 
ers, its capacity for moisture decreases, and a portion of the 
moisture present will be deposited as dew. If the tempera- 
ture falls to 52° F. half of the original quantity will have 
been deposited. Now, suppose the air at 72° F. to have 
been nearly but not quite saturated ; as the temperature is 
lowered, a point will be reached at which the air is satu- 
rated, and then a temperature at which the dew will begin 
to form. This last temperature is called the dew-point. 

The dew-point may be determined with sufficient accuracy 
for ordinary purposes by placing ice in a tin cup containing 
water, and noting, by a thermometer, the temperature of 
the water when the dew begins to form on the outside of the 
vessel. The " sweating" of pitchers is an indication of rain, 
because it shows that the air is nearly saturated with moist- 
ure, which will fall if the temperature of the air is lowered 
below the dew-point. 



204 ELEMENTS OF PHYSICS. 

Our comfort depends largely on the amount of moisture 
present in the atmosphere. If the air is saturated, the per- 
spiration is not carried off from our bodies ; if it is, at the 
same time, warm, we perspire more, and the air is said to 
be sultry. If the air is too dry, the moisture is carried off 
too rapidly from our lips and eyelids, and they become dry. 

311. The temperature at which liquids boil is con- 
stant for the same substance, under like conditions. Sev- 
eral conditions influence the boiling point: 

1. The nature of the liquid. The boiling point of several 
liquids under the pressure of one atmosphere is given below. 

Table of Boiling Points. 

Bromine . . 146°. 4 F. 

Alcohol . . . 173.1 

Water ... 212.' 

Mercury ... 662. 

2. The adhesion of the liquid to the vessel that contains it. 
Water sometimes boils in a glass vessel at 214° F. ; espe- 
cially is this apt to be the case if the water has been 
deprived of air by previous boiling. 

3. Salts in solution increase the boiling point. A satu- 
rated solution of common salt boils at 227° F.; of calcium 
chloride at 355° F. Substances mechanically suspended, 
like sawdust, do not influence the boiling point. The steam 
which forms in the last two conditions assumes almost imme- 
diately the temperature of 212° F. 

4. Variations of pressure. A liquid boils when the tension 
of its vapor is equal to the pressure which it supports. If 
a cup containing ether be placed under the receiver of an 
air-pump, the ether will boil when the receiver is partially 
exhausted. So, also, tepid water may easily be made to 
boil in an exhausted receiver. 



Nitrous oxide 


— 157° F 


Carbonic acid 


— 108.4 


Sulphurous acid 


+ 17.6 


Ether .... 


. 94.8 



BOILING POINT. 



205 




The culinary paradox illustrates the same principle. A 
flask containing boiling water is tightly corked while the 
steam is escaping, and in- 
verted. If, now, cold water 
be poured on the bottom of 
the flask, the boiling will be 
renewed. The reason of this 
is, the cold water condenses 
the steam above the water, 
produces a partial -vacuum, 
and thus diminishes the pres- 
sure on the liquid. 

The sirup of sugar and of 
vegetable extracts are concen- 
trated in closed vessels, called 
vacuum pans. A powerful air-pump constantly removes the 
pressure from the pan, and, consequently, the evaporation 
proceeds at a temperature so low that it secures the sirup or 
the extract from injury by heat. 

312. A variation of an inch in the barometric column 
makes a difference of about 2° F. in the boiling point of 
water. The atmospheric pressure is lowered on ascending 
mountains; hence, water boils at lower temperatures on 
mountains than at the sea level. A difference of 600 feet of 
ascent makes a variation of about 1° F. in the boiling point. 

Under increased pressures the boiling point is raised. If 
water be placed in a small boiler, Fig. 179, furnished with 
a thermometer, a manometer, and a stop-cock, and boiled, it 
will be found that so long as the stop-cock is open the tem- 
perature of boiling will remain steadily at 212° F. On 
closing the cock the boiling point will rise, because the 
steam which continues to form increases in elastic force, and 
produces pressure on the water. When the manometer 



206 



ELEMENTS OF PHYSICS. 




shows a pressure of thirty inches of mercury, the boiling- 
point will equal 249°. 5 F. This is the boiling 
point due to two atmospheres : one shown by 
the manometer; the other, the atmospheric 
pressure present before closing the cock. 

If steam is formed in a boiler and then 
conducted through red-hot tubes, it follows 
the general law for expansion of gases, and 
is then called superheated steam. Such steam 
is applied to the rendering of fats. 

313. Every one must have noticed that 
when drops of water are thrown on a heated 
stove they roll about, becoming gradually 
smaller, and finally disappear in a sort of 
explosion. The explanation of this phenom- 
enon is, that as soon as the drop reaches the 
surface a portion of it is converted into vapor, which sup- 
ports the liquid and prevents it from touching the heated 
metal. The drop assumes what is called the spheroidal state, 

and evaporates at a temper- 
ature lower than its boiling 
point. If a copper flask be 
intensely heated, and a small 
quantity of water poured 
in, the water will assume 
the spheroidal condition, and, 
for a time, all will appear 
quiet. Fig. 180. Now cork 
the flask and remove the 
source of heat. When the 
w flask has sufficiently cooled, 
the water will come in con- 
tact with its surface, and so much steam will be formed 




Fig. 180. 



LIQUEFACTION OF VAPORS. 



207 



suddenly that the cork will be ejected with violence. It is 
probable that boiler explosions are sometimes caused in a 
similar manner. 

There are some curious phenomena which are due to the 
spheroidal state. Thus, if sulphurous acid is throw T n into a 
capsule heated white hot, it assumes a spheroidal state, and 
remains at a temperature of 13° F. Water thrown into it 
will instantly freeze. So, also, a hand moistened with water 
may be drawn without injury through molten iron as it runs 
from the furnace. The moisture forms a non-conducting 
envelope which sufficiently protects the hand during the 
short period of its immersion. 

314. A saturated vapor condenses into a liquid at its 
boiling point. The process of distillation illustrates this 




fact. It is used to separate volatile liquids from mix- 
tures. Fig. 181 represents a common still : the boiler, a, 
contains the liquid to be evaporated; the spiral tube, dd, 



208 ELEMENTS OF PHYSICS. 

which is called a worm, receives the vapors from the boiler. 
The worm is kept cool by being surrounded with cold water, 
and the vapors condense within it and run into a suitable 
receptacle. 

Recapitulation. 

The effects of heat are : 
1- The expansion and contraction of bodies. 

2. The melting and solidifying of solids. 

3. The vaporization and condensation of liquids. 

4. The incandescence and cooling of solids. 



Specific and Latent Heat. 

315. Let us now consider some facts relative to the 
amount of heat which is required to produce changes of tem- 
perature in known weights of different substances. We as- 
sume as a relative measure of the quantity of heat that may 
be gained or lost by a body the thermal unit, which is the 
amount of heat required to raise one pound of water from 
32° F. to 33° F. 

Suppose, now, that we have a uniform source of heat, as 
an alcohol lamp that consumes a pint of alcohol an hour, 
and suppose that in our experiments no heat is wasted in 
heating the apparatus, or the surrounding objects. If we em- 
ploy this heat in warming different substances, we should 
find two sets of phenomena : those of specific, and of latent 
heat. 

Specific Heat. If one pound of water were raised from 
32° F. to 33° F. in a given time, the same amount of heat 
would be competent to raise five pounds of sulphur or 



SPECIFIC HEAT. 209 

thirty pounds of mercury from 32° to 33° F., or would raise 
one pound of sulphur five degrees F. and one pound of mer- 
cury thirty degrees F. The heat required to raise one pound 
of any substance through 1° F., compared with the thermal 
unit, is called the Specific Heat of the substance. 

316. We may determine the specific heat of bodies by 
reversing this experiment. Suppose equal weights of differ- 
ent bodies be heated to the same temperature in a bath of 
boiling water or oil, and then placed in cavities in a cake of 
ice. In comparison with water, sulphur will melt 4-, iron ^, 
and mercury ^ as much ice. These fractions express the spe- 
cific heats of these substances, because the heat given out in 
cooling is precisely equivalent to that required to raise the 
same body through the same number of degrees. 

317. The specific heat of aeriform bodies may be de- 
termined by passing a heated gas through the worm of a 
distilling apparatus, and noting the rise in temperature 
produced in the water when a given weight of gas has 
been cooled to a known temperature. 

318. The specific heat of a substance increases slightly 
with a rise in the temperature, and is generally much 
greater in the liquid state than in either the solid or the 
aeriform condition. These facts are shown in the annexed 
tables. 

Tables of Specific Heat. 

Between Between 

32° F. and 212° F. 32° F. and 5^2° F. 

Mercury 0330 .0350 

Silver 0557 .0611 

Iron 1098 .1218 

Glass 1770 .1900 

Phys. 18. 



210 ELEMENTS OF PHYSICS. 

Aeriform. Liquid. Solid. 

Water 4805 1.0000 .5050 

Bromine 0555 .1060 .0843 

Lead .0482 .0314 

Alcohol 4534 .5050 

Equal volumes. Equal weights. 

Air ' ." . .2375 .2375 

Oxygen 2405 .2175 

Hydrogen .2539 3.4090 

Turpentine 2.3776 .5061 

319. With the exception of hydrogen, water possesses 
the highest specific heat known. The presence of large 
bodies of water has, for this reason, a marked effect on the 
climate, owing to the large amounts of heat which seas 
absorb and emit in accommodating themselves to changes in 
external temperatures. An oceanic climate is, therefore, 
more equable than an inland climate ; its summers are cooler 
and its winters warmer. 

On the islands of Lake Erie, water does not freeze until 
the water of the lake has cooled to 40° F., thus prolonging 
the season sufficiently to ripen grapes. A daily effect 
is witnessed in tropical islands in the land and sea-breezes. 
While the sun shines, the land becomes warmer than the 
ocean, and, by consequence, the air above the land becomes 
rarefied by the heat, and is displaced by the cold air which 
presses in from the ocean, and a sea-breeze is produced ; in the 
night, the land is sooner cooled, the air above it becomes 
more dense and flows out to the ocean in a land-breeze. 

Latent Heat. These facts show that different bodies 
require different quantities of heat in order to increase their 
temperature. Suppose, now, that we employ heat sufficient 



LATENT HEAT. 211 

to melt them or to vaporize them. If a thermometer be 
placed in a basin filled with melting ice, it will remain at 
32° F. until the whole is melted. The temperature will 
then rise to 212° F., and then again become constant until 
all the water is changed to steam. So, generally, a body in 
the act of dianging its state in melting or in vaporizing maintains a 
constant temperature. Now, it is manifest that a considerable 
amount of heat is required to effect these changes, although 
it is not sensible to the thermometer. It performs work by 
overcoming the cohesion of the molecules, and disappears as 
heat. It is, however, capable of re-appearing as heat; for, 
when the vapors change to liquids or the liquids to solids, 
the force of cohesion performs work, and a corresponding 
amount of heat is given out. The heat which a body 
absorbs or gives out in changing its molecular condition is 
termed latent heat. 

320. The latent heat of fusion may be determined by 

the method of mixtures. Suppose a pound of water at 212° 

F. be mixed with a pound of water at 32° F., it will give 

212° -1- 32° 
two pounds of water at ~ = 122° F. ; but, if a 

pound of water at 212° F. be mixed with a pound of ice at 
32° F., we shall have two pounds of water at 51° F. In 
this case the water has lost 212°— 51° == 161° F., while the 
ice has gained 51° — 32° =19° F.; so that 161°— 19° = 
142° F. have disappeared in changing ice to water; or, in 
other words, 142 thermal units are required to change a 
pound of ice into water. 

Latent Seat of Fusion. 

Water 142°.65 F. 

Sulphur 16.85 

Lead 9.65 

Mercury 5.11 



212 ELEMENTS OF PHYSICS. 

The latent heat of water is of the greatest value in nature, 
because (1) it retards the melting of snows. If it were not 
for this provision, the inhabitants of northern valleys would 
be subject to terrific inundations at every approach of spring. 

(2) The melting of ice withdraws heat from surrounding ob- 
jects. Near the Great Lakes, the spring is so much retarded 
by the melting of the winter's ice that, generally, the buds of 
trees do not swell until the danger of late frosts is past. 

(3) The freezing of water mitigates the sudden setting in 
of frosts, as the very act of freezing liberates heat. Hence, 
it is a common remark that the weather moderates on a fall 
of snow. 

321. Freezing mixtures depend on the latent heat which 
is absorbed in dissolving solids. If one part of common 
salt and two of snow are mixed together, the salt causes the 
snow to melt and the water dissolves the salt, so that both 
become liquid and absorb a large amount of heat from sur- 
rounding objects. The temperature may be lowered to — 4° 
F. This is the mixture used in freezing ice-creams. If 
crystallized calcium chloride be mixed with snow, a cold 
of — 50° F. may be produced. This is more than sufficient 
to freeze mercury. 

322. The latent heat of vapors may be determined by 
distilling them and noting the rise of temperature caused 
in the water surrounding the worm on condensing a known 
weight of vapor. The following experiment is a convenient 
method of illustrating the latent heat of water. 

Arrange a glass flask and beaker, as in Fig. 182. Pour 
one ounce of water at 32° F. into the flask, and 5 J ounces 
at the same temperature into the beaker. Now, note (1) 
the time required to raise the water in the flask to boiling 
arid that required to change the boiling water into steam. 
The latter will be 5 J times longer than the former. (2) When 



LATENT HEAT OF VAPORS. 



213 



the water in the flask has been expelled, that in the beaker 
will be raised to 212° F., showing that an ounce of steam 




Fig. 182. 



is competent to raise 5J ounces of water through 180° F. 
Therefore, the latent heat of steam is 180 X 5J = 960°. 

Latent Heat of Vapors. 



Water . 
Alcohol . 
Acetic acid 



966°.6F. Ether .... 162°.8 F. 
374.9 Bisulphide of Carbon 156. 
183.4 Bromine ... 82. 



323. When liquids are evaporated they absorb heat 
from surrounding objects and produce cold. A shower of 
rain cools the air by its evaporation. The more rapid the 
evaporation the greater will be the effect produced. Water 
may be frozen by its own evaporation, by placing a thin, 
shallow capsule, filled with water, over strong sulphuric 
acid, under the receiver of an air-pump. On rapidly ex- 
hausting the receiver, the sulphuric acid absorbs the aqueous 
vapor, and allows a very rapid evaporation of the water, 
which effects the freezing of a portion of it. 
. If a volatile liquid like ether or bisulphide of carbon be 
poured in a watch-glass which rests on a drop of water 
placed on a board, and a rapid current of air be blown 



214 ELEMENTS OF PHYSICS. 

over it, the cold produced by the evaporation will freeze the 
watch-glass to the board. 

324. When vapors are condensed they give out their 
latent heat. Water may be boiled in a wooden tank by 
forcing steam into it. Buildings are warmed by the heat 
of steam generated in a boiler placed in the basement. To 
this end, the steam is conveyed to the several apartments by 
coils of iron pipes. 

Recapitulation. 

The measurement of heat may regard, 

1. The relative intensity Temperature. 

2. The relative quantity Specific heat. 

3. The amount absorbed or emitted during molecular 

changes Latent heat. 



The Distribution of Heat. 

325. The effects of heat thus far considered have refer- 
ence only to the molecular motions which take place within 
a heated body; we are now to consider how heat may be 
transferred to other bodies. In the first place, we remark 
that no body is known to exist at a temperature of absolute 
zero; that is, at a temperature in which its molecules are 
absolutely at rest with respect to each other. Hence, all 
bodies possess some heat. In the second place, we notice 
that any body assumes, sooner or later, the temperature of 
surrounding bodies. Now, this can occur only by a con- 
tinued exchange of molecular motions, by virtue of which 
every body emits thermal waves or vibrations of some degree 
of intensity, while, at the same time, it receives other ther- 
mal waves from surrounding bodies. If the sum of the 



TRANSFER OF HEAT. 215 

motions received is less than that emitted, the body becomes 
colder; but, if greater, the body becomes warmer. If it 
receives back just as much heat as it gives out, it remains 
at a uniform temperature. 

326. Heat may be transferred from one body to another 
in three ways : 

1. By conduction, or from molecule to molecule. 

2. By convection, or by molecules moving in currents. 

3. By radiation, or by thermal undulations through space. 

327. The conductibility of solids may be shown by 
equal -sized rods, along which a number of marbles are 
fastened, at equal distances, 
with wax. Fig. 183. If one 
end of the rod be in contact 



IBBl"- -V: i ~ llllfllllli 




with a heated body, the mar- <e 
bles will drop off one after 
the other as the different sec- 
tions of the rod attain the FlG * 183 * 
temperature of the fusing point of wax. Different sub- 
stances will show different conducting power, but in all 
cases it will be found that the transference of heat by con- 
duction is a process comparatively slow. Porous solids are 
poor conductors ; liquids and gases almost non-conductors ; 
many of the metals are good conductors. 

Relative Thermal Conductivity. 

Silver 100. Iron 11.9 

Copper 73.6 Lead 8.5 

Gold 53.2 Platinum 8.4 

Brass 23.6 Bismuth 1.8 

328. That liquids are poor conductors may be shown 
by passing the tube of an air-thermometer through a funnel, 



216 



ELEMENTS OF PHYSICS. 



so that the bulb shall be just below the surface when the 
funnel is nearly filled with water. Fig. 184. Now, if ether 
be poured on the water and ignited, 
the thermometer will be but slightly 
affected. 

329. The conducting power of a 
body may be roughly estimated by 
the touch. An iron rod heated above 
120° F. will burn the hand, because 
it conveys its heat rapidly to the 
skin, and if cooled below 0° F. it 
will blister the lips, because it con- 
veys their heat away so rapidly. An 
oil-cloth feels warmer or cooler than 
a carpet in the same room accord- 
ing as their common temperature is 
greater or less than that of the skin. 
So, also, a person clad in woolen gar- 
ments may enter an oven heated to 300° F. without incon- 
venience, because both his garments and the air are poor 
conductors. 

Water is sooner heated in a tin cup than in one of por- 
celain, because the metal is a better conductor of heat. 
Porous bodies, like ashes and plaster of Paris, are such poor 
conductors that if the hand be protected by a thin layer of 
either, it may carry live coals without danger. 

330. Non-conductors are used (1) to prevent the 
escape of heat, or (2) to exclude heat. 

1. Double doors and windows, which inclose a layer of 
air, prevent the escape of heat from our apartments. Cloth- 
ing prevents the escape of heat from our bodies. The con- 
ducting power of the ordinary materials used is in this 
order : linen, cotton, silk, wool, furs. Hence, with equal 




Fig. 184. 



CONVECTION. 



217 



texture, a woolen garment is warmer than one of silk, 
cotton, or linen. 

2. Furnace men wear thick woolen garments to exclude 
heat, because that to which they are exposed is greater than 
the heat of their bodies. Ice may be kept from melting by 
wrapping about it a thick blanket. Ice-houses have double 
walls, inclosing a thick layer of straw, sawdust, or charcoal. 
Water-coolers are constructed in the same manner. 

331. Convection. If heat be applied to the bottom of 
a flask of water, (Fig. 185), con- 
taining matter in suspension, as 
sawdust, up and down currents will 
be formed. The particles of the 
liquid which become heated ex- 
pand and rise, because the colder 
and heavier particles descend and 
force them upward. This process 
of circulation among molecules is 
termed convection. 



332. The convection of gases 
is more energetic than that of 
liquids, because their expansion by 
heat is much greater. If "touch- 
paper" containing potassium chlo- 
rate be burned in the vicinity of a heated body, the cur- 
rents of air arising from it may be traced in the smoke. 




Fig. 185. 



The air which thus rises is heated by convection. 

333. In all cases of convection there must be two cur- 
rents in opposite directions. If a lighted candle be held in 
the crack of a door which opens between two apartments of 
different temperatures, a current of warm air from the 
heated room will drive the flame outward, if held at the 

Phys. 19. 



218 ELEMENTS OF PHYSICS. 

top of the door ; and a current of cold air will drive the 
flame inward, if held at the bottom of the door. 

The winds are primarily due to interchange of air between 
localities unequally heated. Only the lower current admits 
of being accurately traced, but we have ample evidence that 
there are also upper currents. It frequently happens that 
clouds are seen moving in different directions — the lower 
clouds in the direction of the surface-winds, and the upper 
clouds in the opposite direction. 

334. The heat of the sun can not reach the earth by 
conduction nor by convection, since heat is propagated by 
either of these methods very slowly. In our study of the 
solar spectrum we learned that the least refracted end of 
the spectrum contained invisible rays which had the power 
of affecting the thermometer. These dark rays must reach 
us in the same way that light reaches us; that is, by ther- 
mal waves, which are transmitted by the aether and other 
media. Heated bodies have the same power of emitting 
thermal waves in all directions that luminous bodies have 
of emitting luminous waves. This emission of heat is 
termed radiation. The phenomena of radiant heat and light 
are, in all respects, similar ; and, with the necessary change 
of terms, their laws are identical. 

The laws of radiant heat are: 

1. Heat radiates in straight lines in all directions, 

2. The intensity of radiant heat is inversely as the square of 
the distance from its source. 

3. The intensity of radiant heat is proportional to the temper- 
ature of its source. 

335. Radiant heat, incident on a surface, may be (1) 
reflected, (2) refracted, (3) absorbed, or (4) transmitted. 

336. Substances which reflect light well are also good 



REFRACTION. 219 

reflectors of heat. The polished metals are all good reflect- 
ors of heat. Archimedes is said to have burned the Romau 
fleet at Syracuse by concentrating upon the ships the solar 
rays by means of concave mirrors. 

337. When a solar beam is transmitted through a prism 
of rock-salt, and the spectrum is examined by a thermom- 
eter, we have the result sketched in Fig. 167, showing: 

1. That the thermal spectrum extends through and be- 
yond the visible spectrum. Thermal waves must, therefore, 
be of different refrangibility and wave length. 

2. The maximum heating effect lies beyond the red, in 
rays of great wave length, but invisible to the eye. 

The thermal waves which accompany light are called 
luminous thermal waves, and the dark rays are called obscure 
thermal waves. When a platinum wire is heated it emits, at 
first, only obscure rays ; when it becomes incandescent, it 
not only emits luminous rays, but adds to the intensity of 
the obscure vibrations. 

338. Most transparent bodies transmit the rays of heat 
from the sun as well as those of light, but will not equally 
transmit the thermal rays from artificial sources. Thus, the 
heat of the sun will readily pass through glass windows and 
warm a room, w T hile the same thickness of glass would 
effectually shut off the heat of a fire. On the other hand, 
there are bodies that are opaque to light which transmit 
the dark rays of heat almost perfectly ; such, for example, 
is a solution of iodine in bisulphide of carbon. A sub- 
stance which transmits heat is called diathermanous ; one 
that is opaque to heat is called athermanous. Rock-salt is 
one of the most diathermanous substances known. A lens 
made of rock-salt will so concentrate the obscure thermal 
rays that they may be made to melt and even ignite solid 
bodies. 



220 ELEMENTS OF PHYSICS. 

The incident rays of heat which are not reflected or 
transmitted are absorbed. Only the rays which are ab- 
sorbed have any effect in warming the body on which they 
fall. Dry air is almost perfectly diathermanous, but air 
containing moisture has far less power of transmitting lumi- 
nous thermal rays, and is almost athermanous for obscure 
thermal rays. The solar rays pass with comparative ease to 
the earth, and are expended in warming its surface. The 
heated earth radiates only obscure rays, which are absorbed 
by the atmosphere, and, consequently, its rate of cooling 
is diminished. In central Asia the air is very dry, and the 
radiation from the earth is so rapid that the nights are 
very cold and the winters almost unendurable. 

The hot-beds of gardeners act by economizing the heat 
of the sun. The solar rays pass freely through the glass 
and are absorbed by the earth and the plants. These emit 
only obscure rays, which can not escape through the glass. 
The air confined in the bed attains a temperature above 
that of the exterior atmosphere. 

339. If a body is athermanous all the rays of heat 
which fall upon it that are not reflected are absorbed. 
Hence, bad reflectors are good absorbents and are readily 
warmed. As bodies must give out, in cooling, the heat 
which they have absorbed, so good absorbents are good radi- 
ators. The relation between the radiating, reflecting, and 
absorbent powers will be seen by the following table : 

Reflection. Absorption. Radiation. 

Lamp-black 100 100 

Indian ink 4 96 85 

White lead 47 53 100 

Isinglass 48 52 91 

Gum lac 57 43 72 

Polished metal 86 14 12 



RADIATING POWER. 221 

The radiating power of a body is dependent more on 
the nature of its surface than of its substance. If a tin can- 
ister have one of its sides coated with lamp-black, another 
with paper, a third scratched or tarnished, and the fourth 
polished, and be filled with boiling water, its sides will, of 
course, have the same temperature ; but they will differently 
affect a thermometer placed in succession hear each face, 
according to the difference in their radiating power. 

Lamp-black has the highest emissive power known ; the 
polished metals are the poorest radiators. Hence, a bright 
silver tea-pot filled with hot water will retain its tempera- 
ture longer than one of earthemvare. 

340. Franklin found by placing pieces of cloth of the 
same texture, but of different colors, upon newly fallen 
snow, that the snow melted under the cloth with greater 
rapidity the darker the tint. This fact shows that, for solar 
rays, clothes of dark color are better absorbents and poorer 
reflectors than w r hite. Other experiments show that this 
difference in the absorptive effect of colors entirely fails for 
heat from artificial sources. It so happens that many good 
reflectors are white, and many good absorbents and radiators 
are dark; but their respective powers are due rather to the 
molecular condition of their surfaces than to their colors. 



Recapitulation. 

( Conduction. 

Heat may be transferred by < Convection. 

I Radiation. 

r Reflected. 

Radiant heat, incident on a J Absorbed. 

body, may be J Refracted. 

V. Transmitted. 



222 ELEMENTS OF PHYSICS. 



The Sources of Heat. 

341. The sources of heat may be comprised in three 
classes: (1) physical, (2) chemical, (3) mechanical. 

The principal physical sources are the sun and the 
fixed stars. It has been calculated that, if the earth had 
no atmosphere, the solar heat received by the earth in one 
year would melt a layer of ice, completely enveloping it, to 
the depth of one hundred feet. It has also been estimated 
that the earth receives from the fixed stars about four-fifths 
of this amount. These are the ultimate sources of most of 
the available heat of the globe. Were either of these cut 
off, the life of the globe would soon be destroyed. 

342. When any two bodies unite in chemical combina- 

m 

tion heat is usually evolved. Combustion is the rapid com- 
bination of two or more substances, attended by the evolu- 
tion of heat, and generally of light. If a grain of iodine 
be placed on a slip of phosphorus they will kindle into a 
flame, which will afterward be continued by the oxygen of 
the air. 

343. Ordinary combustion is due to the union of the 
oxygen of the air with the carbon and hydrogen contained 
in the coals, oils, and gases of our fires and flames. The 
rusting of iron and the decay of w r ood, are examples of slow 
combustion with oxygen. A log of wood in decaying 
evolves the same amount of heat that it does in burning, 
although the combustion takes place so slowly that no in- 
crease in temperature is perceptible. 

Animal heat is due to slow combustion. In respiration (1) 
oxygen passes by osmosis through the cell walls of the lungs, 
and is absorbed by the blood ; (2) this blood is then carried 



MECHANICAL SOURCES OF HEAT. 223 

to the capillaries of the different organs, where the oxygen 
unites with the carbon of the tissues and forms carbonic 
acid ; (3) the blood then returns to the lungs charged with 
this carbonic acid; (4) the carbonic acid is then exhaled by 
osmosis, and a fresh supply of oxygen absorbed. 

The supply of carbon in the tissues is maintained by the 
processes of digestion and nutrition. Thus, in one sense, our 
animal heat is maintained by the indirect combustion of 
food and air. 

344. The mechanical sources of heat are percussion, 
compression, and friction. (1) If a nail be pounded on an 
anvil with rapid blows, it may be made red-hot by percus- 
sion. (2) The production of heat by the compression of 
gases may be shown by the pneumatic syringe, Fig. 186. 




Fig. 186. 

This instrument consists of a stout tube in which a piston 
works air-tight. To use it, a piece of tinder is placed on the 
bottom of the piston, which is then driven suddenly down 
the tube. The air in the tube is compressed, and liberates 
so much heat as to set fire to the tinder, which is seen to 
burn when the piston is withdrawn. 

(3) The friction of two bodies always produces heat. It 
is the heat produced by friction that ignites the phosphorus 
on the end of a match, and that causes the axles of car- 
wheels to become hot. Savages procure fire by revolving 
the end of one piece of wood in the cavity of another. 

An experimental demonstration of the same fact n ay be 
shown by attaching to a whirling table a brass tube filled 
with water, and corked. Fig. 187. If, when the tube is 
revolving rapidly, a clamp, P, of two pieces of oak is 



224 ELEMENTS OF PHYSICS. 

pressed against the tube, the heat evolved by the friction 
of the clamp will be sufficient to boil the water in a few 
minutes. 




Fig. 187. 

345. These facts are in accordance with the dynamical 
theory of heat, which assumes that heat is a kind of energy 
which produces molecular motion. In all cases of percus- 
sion, compression, and friction, a certain amount of mechan- 
ical energy is arrested, and its visible motion is destroyed. 
At the same time heat is produced. That is, the energy of 
visible motion is transformed into the energy of molecular motion, 
which is heat. 

Conversely, heat is consumed in effecting mechanical work. 
Let a cylinder filled with compressed air be cooled to the 
temperature of surrounding bodies. Its elastic force is com- 
petent to perform mechanical work (1) by moving a pis- 
ton, and (2) by displacing the air in front of the piston. 
If the air be allowed to expand so as to perform work, it 
will be, at the same time, chilled, because its molecular 
energy is transformed into the energy of visible motion. 



JOULE'S EQUIVALENT. 225 

346. There is a constant numerical relation between 
the energy of visible motion and the energy of molecular 
motion, which is known as Joule's equivalent, and is thus 
expressed : The amount of heat required to raise one pound 
of water 1° F. is competent to lift 772 pounds one foot high. 
The converse is also true ; if 772 pounds be dropped one 
foot it will develop sufficient heat to raise one pound of 
water 1° F. 

347. If we know the weight and velocity of any 
moving body, we can calculate the amount of heat which 
would be generated by suddenly stopping it. It has been 
calculated that if the earth were stopped in its orbit, it 
w T ould develop heat equal to that derived from the com- 
bustion of fourteen equal -sized globes of coal. If, then, 
it should fall into the sun, it would generate by the collision 
heat equal to that evolved by the combustion of 5,600 equal 
worlds of solid carbon. 

These considerations have led some philosophers to the 
conclusion that the solar heat is maintained by the falling 
of meteoric masses into the body of the sun. If the earth 
should strike the sun, the heat developed by the shock 
would be sufficient to equal the solar radiation for a 
century. 

348. The dynamical theory of heat also explains the 
phenomena of expansion and of latent heat. Thus, when 
heat enters a body, its actual energy is employed (1) in 
increasing the intensity of molecular motion, which is shown 
by a rise in the temperature ; (2) this also separates the 
molecules and produces expansion; (3) a sufficient heat 
melts or vaporizes the body. The latent heat required is 
the energy necessary to overcome cohesion ; that is, it per- 
forms work in separating and re-arranging the position of the 
molecules. The latent heat which disappears is not lost, 



226 ELEMENTS OF PHYSICS. 

but has been employed in giving the molecules new posi- 
tions. If the vapor returns to the liquid state, or a liquid 
to the solid state, an equal amount of heat will be given 
out, because interior work has been performed by cohesion, 
which draws the molecules closer together, and is trans- 
formed into sensible heat. 

We may roughly compare latent heat with mechanical 
energy. If I throw a stone to a roof sixteen feet high, I 
shall need to give to it a velocity of thirty-two feet per 
second. While the stone rests on the roof it produces only 
pressure, but it is evident that should it fall, it will again 
attain a velocity of thirty-two feet per second before it 
strikes the ground. Therefore, the stone, w r hile on the roof, 
has a possible energy due to its position. So, also, if I melt 
a body I shall require to expend a certain amount of sensi- 
ble heat ; but, in so doing, I shall confer upon the mole- 
cules a possible or potential energy of position, which will be 
again transformed into the sensible energy of heat when the 
melted body solidifies. 

349. Force may be changed but not annihilated. 

The sun is the ultimate source of the available forms of 
energy with which we are surrounded. Let us consider a 
few of the ways by which sunshine may be transmuted and 
preserved. 

1. The mechanical energy of the winds, of falling water, 
and of running streams, is due to the joint action of gravi- 
tation and of the solar heat. A part of this energy may be 
made to re-appear as heat by friction. Thus, a large room 
has been warmed by the friction of two plates, made to re- 
volve by machinery driven by a fall of water. 

2. Plants grow by reason of the light and heat of the 
sunshine, and accumulate a supply of fuel and of food. 

(a.) Wood and mineral coal are, therefore, transmuted 






CONSERVATION OF FORCE. 227 

sunshine. In combustion, the heat re-appears as heat, or it 
may be applied as a moving force for engines. 

(6.) Food is transmuted by animals into animal heat and 
muscular energy, or stored up as flesh. Beef and mutton 
are, therefore, due to solar rays twice transmuted. 

Recapitulation. 

The sources of heat are — 

- -p,, , f The sun. 

1. Physical . < 

( The fixed stars. 

2. Chemical Combustion. 

f Compression. 

3. Mechanical ■{ Percussion. 

V Friction. 

Problems. 

1. How much will a railway track 100 miles long expand on 
being heated from 32° F. to 96° P. ? 

2. How many thermal units are required to raise 80 pounds of 
water from 32° F. to 212° F.? Suppose a pound of coal, if econom- 
ically burned, to have this thermal power, how many pounds of 
mercury can it raise through the same temperature? 

3. How many pounds of ice at 32° F. would the same fuel melt? 
How many pounds of w T ater at 212° F. would it change into steam? 

4. From the table on page 199 calculate the relative lengths of 
silver and platinum which should be taken to construct a gridiron 
pendulum. 



CHAPTER XVI. 

ELECTRICITY. 

350. One of the earliest physical facts recorded in the 
history of science, is that when amber is rubbed with silk, 
it acquires the property of attracting to itself light bodies, 
and then of repelling them. Within the past century, phi- 
losophers have found that these are but particular manifesta- 
tions of a force which is constantly evoked in all kinds of 
molecular changes, and whose phenomena are among the 
most wonderful in nature. This force is electricity. It is 
convenient to study its phenomena under three divisions: 
(1) Magnetism, (2) Statical Electricity, (3) Dynamical 
Electricity. 

The Phenomena of Magnetism. 

351. It has long been known that a certain ore of iron, 
called the loadstone, has the property of attracting iron 
filings. Because this ore was first found near Magnesia, a 
city of Asia Minor, loadstones are called natural magnets. 
Bars of hardened steel may be converted into artificial mag- 
nets far more powerful than natural magnets. 

352. If a magnet be rolled in iron filings, the filings 
will cling to it, but especially at the ends. Fig. 188. These 

ends are termed the poles of the mag- 
net. The force residing in a magnet 
is called magnetism. 

Fig. 188. If a sheet of stiff paper be laid 

upon a bar magnet, and iron filings be sifted evenly upon 

(228) . 




MAGNETISM. 



229 






the paper, the particles of iron will arrange themselves in 
curved lines about the poles. Fig. 189. If a magnetic bar 
or needle be poised at its center so that it will swing freely, 






v\\l Hi////. 



;Miip 







.^. . -;. _ 






;',v,wfe 






WW 




Fig. 189. 

one end will point toward the north and the other toward 
the south ; hence, one end is called the south and the other 
the north pole of the magnet. 

353. Either pole will equally attract iron filings ; but 
if two magnets are brought near each other, it will be found 
that the north pole of one will attract the south pole of the 
other. If, however, two sim- 
ilar poles are brought near 
each other, a repulsion takes 
place. Fig. 190. Hence, this 
law : Like poles repel and unlike 
poles attract each other. 

354. If a long steel needle 
be magnetized, the center will 
exhibit no magnetic force and 
is said to be neutral. If the 
needle be broken, each half 
will be found to be a magnet 
with two equal and opposite poles. If this division be con- 
tinued, no portion can be obtained so small that it will not 
be a perfect magnet. We, therefore, conclude that every 




Fig. 190. 



230 



ELEMENTS OF PHYSICS. 



magnet is a collection of polarized particles having their 
similar poles turned in the same direction. 

We may represent this state of polarity in a magnet by 
Fig. 191, in which the alternate black and white spaces 




Fig. 191. 
represent the polarity of each particle. All the north poles 
are disposed in one direction (the black spaces) and all the 
south poles (the white spaces) in the opposite. The opposite 
polarities balance each other at the center, which thus re- 
mains neutral, but are strongly manifested at the ends. 

355. If a rod of soft iron, Fe, Fig. 192, be brought 
near one of the poles of a magnet, M, the two ends of the 

N> Fe &_ JST ___ M S 




Fig. 192. 
rod will also be able to attract iron filings. The rod becomes 
a temporary magnet, but it will lose its magnetic properties 
soon after it is taken away from the presence of the magnet. 
The influence by virtue of which a magnet can develop 
magnetism in iron is called induction. We may suppose 
that, in its ordinary state, the molecules of the iron rod are 
all indued with magnetism, but that they are so arranged 
that the opposite forces neutralize each other ; and that the 
presence of the magnet in some way so modifies the sur- 
rounding region that the molecules of the iron assume the 
polarized state of the magnet as* represented in Fig. 191. 
The inductive force is greatest when the magnet is in con- 
tact with the iron. If a steel bar be in contact with a 
magnet, its particles become polarized very slowly; but 



MAGNETS. 



231 



when once acquired, its magnetism is permanent. Magnet- 
ism may be sooner induced in steel by rubbing it with one 
of the poles of a magnet. In this way the ordinary mag- 
netic needles are prepared, but the more powerful magnets 
are produced by means of the voltaic current, as will be 
described hereafter. It is important to notice that in in- 
duction there is no transfer of any force, but merely a devel- 
opment of polarity among the particles of the body acted 
upon. 

A magnetic battery consists of a number of magnets joined 
together with their similar poles in contact. The common 
form is that of a horse-shoe. Fig. 193. When 
a magnet exerts its inductive power on a piece 
of soft iron, its own magnetic intensity is tem- 
porarily increased. For this reason the mag- 
net is provided with a keeper or armature, K, 
of soft iron. 

356. Iron, steel, nickel, and cobalt are 
the only substances in which magnetism can 
be developed by ordinary induction. Man- 
ganese and a few other substances are also 
attracted by very powerful magnets. xlll 
these are called magnetic substances. If a Fig. 193. 
magnetic substance is suspended by a string between the 
poles of a horse-shoe magnet it will take a position in the 
direction of the line which joins the two poles of the 
magnet. 

On the other hand, there are a great number of sub- 
stances which, if similarly suspended, will assume a position 
at right angles to the line joining the poles, as if repelled 
by them. Such substances are called diamagnetic. Among 
diamagnetic substances are phosphorus, bismuth, antimony. 
The diamagnetism is not permanent. 




232 ELEMENTS OF PHYSICS. 

357. The earth acts as a magnet. The magnetic 
needle, which is of almost priceless value to mariners, points 
toward the magnetic poles of the earth. These magnetic 
poles are near, but do not coincide with the geographical 
poles of the earth. Hence, the needle will point in a due 
north and south line only when the magnetic meridian coin- 
cides with the geographical meridian. This is very nearly 
the case at Cleveland, O., but in New York the needle 
points west of north and in Chicago east of north. More- 
over, the magnetic poles are slowly shifting their position 
westward, so that the magnetic meridian does not remain 
constant. The deviation of the needle from the geograph- 
ical meridian is called the declination of the needle. 

Recapitulation. 



Magnets are 
Substances , 



Natural or artificial. 
Permanent or temporary. 

Attracted by magnets are . . Magnetic. 
Repelled by magnets are . . Diamagnetic. 



The Phenomena of Statical Electricity. 

358. An electric pendulum is a pith ball attached, by a 
silk thread, to a glass support. If a stick of sealing-wax 
be rubbed with dry flannel and brought near the pith ball, 
Fig. 194, the latter is instantly attracted, but is soon 
repelled. If, now, a warm glass rod be rubbed with a 
silk handkerchief and presented to the ball, the same phe- 
nomena of attraction and repulsion will be observed. 

It will now be found that when the ball has been re- 



STATICAL ELECTRICITY. 



233 




Fig. 194. 



pelled by the glass, it will be attracted by the wax ; and 
when again repelled by the wax, it will be attracted by the 
glass. If the glass and wax be placed on opposite sides of 
the ball, it will vibrate between them by the alternate 
attraction and repulsion of 
each. It is, therefore, evi- 
dent that the glass and wax 
manifest similar and yet op- 
posed properties. These prop- 
erties, thus excited by fric- 
tion, are due to electricity. 

359. Electricity is a force 
which becomes manifest by 
its peculiar phenomena of at- 
traction and repulsion. It is 
now regarded as a mode of 
molecular motion which is always manifested in two opposite 
or polarized states. That developed on the glass is called 
positive, (+), and that on the wax, negative electricity, ( — ). 

Formerly, electricity was supposed to be due to the presence 
or absence of a single electrical fluid, or to the presence of 
two electrical fluids. There is, however, no evidence of the 
existence of any electrical fluid. Ne\ ertheless, many of the 
terms of the fluid theory are still in common use, and are 
convenient for describing most electrical phenomena, although 
the meaning attached to them is taken in a sense different 
from that originally intended. 

360. In the preceding experiment we suppose that the 
w T ax became negatively electrified by friction, and, on con- 
tact, transferred a portion of this force to the ball. The 
ball thereby became electrified or charged with negative 
electricity and the two bodies separated. On bringing the 
charged ball near the positively electrified glass the two 

Phys. 20 



234 



ELEMENTS OF PHYSICS. 



were attracted, because of their different electrical states. 
The glass then communicated enough of positive electricity 
to neutralize the negative electricity of the ball, and, also, 
to render it positively charged. The ball was then repelled 
by the glass and attracted by the wax, and so on through a 
series of attractions and repulsions. From these experi- 
ments we derive the following law : Two bodies charged ivith 
like electricities repel each other; two bodies charged with opposite 
electricities attract each other. 

361. Electricity is transmitted from one body to an- 
other with different degrees of rapidity. Those substances 
that transmit electricity readily are called conductors; those 
that do not, are called non-conductors or insidators. In the 
following list the substances named are arranged in the 
order of their conducting power. Those midway in the list 
may be termed semi-conductors or semi-insulators. 



1. The metals, 

2. Charcoal, 

3. Graphite, 

4. Acids, 

5. Water, 

6. Linen, 



Semi-conductors. 

7. Ether, 

8. Dry wood, 

9. Paper, 

10. Dry ice, . 

11. Caoutchouc, 

12. Air and gases, 

Semi-insulators. 



13. Furs, 

14. Silk, 

15. Glass, 

16. Wax, 

17. Shellac, 

18. Ebonite. 

Insulators. 



362. In order that a charged body may retain its 
electrical force, it must either be a non-conductor, or be 
insulated by being supported on non-conductors. The most 
common insulators are made of glass. Baked wood covered 
with shellac varnish will answer very well. Dry air is 
necessary for insulation. In a damp room a film of moist- 
ure gathers upon the apparatus and forms a conducting 
surface. 



ELECTROSCOPE. 235 

363. Electricity is produced whenever two dissimilar 
substances are rubbed together. The reason why it is not 

lore frequently manifest is because it is carried off as fast 
it is developed. When the electrical force is sufficient 
force its way through a bad conductor a spark may be 
produced. In dry, frosty weather, a person, by shuffling 
about a warm, carpeted room, may develop electricity suffi- 
cient to emit a spark from his finger capable of igniting a 
jet of gas. 

364. Both kinds of electricity are always simultane- 
ously produced. If two insulated disks of dry wood, one 
covered with shellac and the other wdth silk, are rubbed 
together and separated, the shellac will manifest positive 
and the silk, negative electricity. Any substance in the 
following list, when rubbed by any one succeeding it, be- 
comes positively electrified, and by any one preceding it, 
negatively electrified : 

-f Cat's-fur, flannel, smooth glass, cotton, paper, silk, the 
hand, sealing-wax, rough glass, sulphur, ebonite, — . 

Thus paper becomes positively electrified when rubbed 
with silk and negatively electrified when rubbed with 
flannel. 

365. The electricity which is produced by friction is 
called frictional electricity. There are, however, other modes 
of producing the same electrical phenomena. It is also 
called statical electricity, because it may be retained for a 
time upon an insulated body. 

An electroscope is an instrument used to detect the presence 
and determine the kind of electricity in any body. 

The simplest is some form of the electric pendulum. The 
gold-leaf electroscope, Fig. 195, consists of two strips of 
gold-leaf, suspended in a glass vessel by means of a metallic 
rod which terminates in a knob or a plate. Within the 



236 



ELEMENTS OF PHYSICS. 



vessel are two metallic posts connected with the ground, 
which serve to remove an excessive charge from the leaves. 

If the knob be touched with 
an electrified glass rod, the 
leaves will diverge, because 
they become charged with pos- 
itive electricity. If, now, any 
electrified body be brought 
near the knob, the kind of 
electricity in the body may 
be determined by its influence 
on the gold-leaves ; for, if the 
electricity be positive, the 
leaves will diverge farther, 
but, if negative, they will 
collapse. 

366. Electrified bodies influence bodies at a distance 

in a manner similar to the action of a magnet on magnetic 

substances. This influence is called electrical induction; and 

the resulting effect, induced electricity. 

C 

A JL1 B 




Fig. 195. 




Fig. 196. 



Let A B be a conductor of brass, insulated on a glass pillar 
and furnished with a number of pith ball electroscopes. 
If this is brought near an electrified body, C, but not so 



INDUCTION. 237 

near as to receive a spark from it, the balls will diverge as 
shown in Fig. 196. By means of the gold-leaf electroscope 
we may ascertain that the nearer end, A, of the conductor 
contains electricity opposite to that of the electrified body, 
C, and the further end, B, the same kind. If C be posi- 
tively charged, its effect will be to repel the positive elec- 
tricity toward the end, B> and to attract negative electricity 
to the end, A. 

367. The two electrical forces may be separated by in- 
duction. Suppose the conductor, A B, to be made of three 
parts, each insulated and movable, and while the whole is 
under the influence of a positively electrified body, let the 
central portion be removed. (1) This part will either yield 
no spark or a very feeble positive one. (2) The portion, B, 
may be discharged by bringing the hand near it, yielding a 
spark of positive electricity. Its electricity is, therefore, 
free to diffuse itself. (3) So long as A and C remain near 
each other neither will be completely discharged on touch- 
ing it separately, because their mutual attractions tend to 
retain their opposite electricities. Electrical forces in this 
condition are said to be bound or disguised. If the two are 
separated, A will yield negative and C positive electricity. 
If communication is made between them, both will be dis- 
charged by the union of their opposite forces. 

If the cylinder, AB, while near the positive ball, C, be 
touched by the hand, the pith balls at A will diverge fur- 
ther — those at B will collapse. As the hand and body are 
conductors, the positive electricity will be repelled to the 
earth. The negative can not escape being bound by the 
attraction of the positive ball, C. On the contrary, it will 
increase, because the inductive force of C was previously 
opposed by the positive electricity accumulated in the end, 
B. If the hand be first removed from the cylinder and 



238 



ELEMENTS OF PHYSICS. 



then the inducing body, the cylinder will remain negatively 
charged. 

Therefore, a body may be charged by induction, or by 
conduction. In conduction there is a transfer of either 
force from an electrified body to another body. In induc- 
tion there is no transfer of force; but an excited body 
induces both kinds of electricity in an insulated body, which 
remains charged with the opposite electricity if uninsulated, 
for a time, in the presence of the excited body. 

368. The electrophorus, Fig. 197, consists (1) of a cake 
of resinous matter, R, resting on a conducting plate of tin, 
and (2) a movable metallic 
cover, T, provided with an in- 
sulating handle, G. If the re- 
sinous cake be beaten with cat's 
fur it becomes charged with neg- 
ative electricity. If, now, the 
cover be placed on the cake, 
its condition is that of an insu- 
lated conductor in the presence 
of an electrified body. Its lower 
surface becomes positive and its upper negative by induc- 
tion. The cake does not discharge itself into the Cover, 
because (1) of the inequalities of its surface and (2) because 
of its non-conducting power. 

If the cover be uninsulated for a moment by touching it 
with the finger, the negative force passes to the ground, 
while the positive is held bound by the negative electricity 
of the resin. Now, if the finger be first removed, and then 
the cover raised by its insulating handle, G, its positive 
electricity diffuses itself over its surface, and the cover will 
yield a positive spark when it is brought near a conductor. 

As the cake acts only by induction, when once charged it 




Fig. 197 



INDUCTION. 239 

retains its electricity for a long time, and may be made to 
induce any number of successive charges in the disk. 

369. To explain the action of induction we may sup- 
pose that whenever a body is electrified, the molecules of 
the surrounding medium become polarized. Thus, if C 
represent a charged body, the adjacent molecules of air, 



as a, b, c, d, will become polar- q a b c d 
ized. Fig. 198. The mole- ffk ^\ 3 J* £T 

^^ r* r* r± r± — 



3 (• (* (M B 



cules of any insulated con- ^^^ (\ (\ (% rk 
ductor, as A B, within their fig. 198. 

influence will also become polarized ; but as they are con- 
ductors they will discharge their electrical forces one into 
the other, and thereby the cylinder itself will become polar- 
ized, as if it were a huge molecule. 

370. Induction takes place in most, if not all, elec- 
trical phenomena. 

I. In attraction. The pith ball of the electrical pendulum 
is first polarized, like the cylinder, AB, Fig. 198. The side 
next the excited glass rod becomes negative by induction, 
and as soon as the attraction of the opposite electrical forces 
becomes greater than the repulsion of the positive electric- 
ity on the further side of the ball, the ball flies to the rod. 

II. In charging. In Figs. 196, 198, suppose C positively 
charged to be brought toward AB. The polarization of 
A B will rise higher and higher in proportion as C comes 
nearer. When C is near enough, A B will become charged 
with positive electricity either by spark or by contact. The 
most probable explanation of this is, that at a high state of 
polarization the adjoining particles discharge their electrical 
forces into each other. By the spark or by contact, an 
equal amount of the two electricities combine and become 
neutral, and the cylinder becomes charged, not by receiving 
more positive electricity, but by discharging its negative. 



240 



ELEMENTS OF PHYSICS. 



III. In discharging. If, now, the hand be brought near 
the positively charged conductor, the electricity of the hand 
is polarized. Its positive electricity passes to the ground, 
and its negative to the fingers. At contact, the negative of 
the hand and the positive of the cylinder combine, and the 
molecules of the cylinder become neutral or unpolarized. 

371. The molecules of conductors are easily polarized 
and discharged : the molecules of insulators require a greater 
force to effect polarization and discharge. Magnetic and 
electrical induction are similar. The induction of magnetism 
in soft iron is rapid but temporary ; that of steel is slower 
but permanent. In magnetic induction, however, the two 
forces can not be separated. In electrical induction, a body 
may be charged positively or negatively; but this can be 
effected and maintained only when it is surrounded by insu- 
lating molecules in which the opposite force is induced. 
Hence, the two forces are always present, and electricity, 
like magnetism, is a polar force. 

372. Electricity is found only on the surface of an 

insulated body. Let a brass ball be suspended by a silk 




Fig. 199. 



thread and be closely covered by two hemispheres of brass. 
Fig. 199. Now, if a charge be communicated to the ap- 
paratus, and then the hemispheres be withdrawn, the elec- 



ELECTRICAL APPARATUS. 241 

ricity will be found only on the hemispheres. This is a 
consequence of the repulsion of like electricities. Another 
result is that the charge tends to escape from bodies ; hence, 

373. The charge will be distributed uniformly only 
on spherical surfaces. On cylindrical surfaces, the charge 
will be accumulated at the ends. If the ends are mere 
points, there will be so great an increase of electrical inten- 
sity that the body will be discharged with great facility and 
generally without the passage of a spark. Hence, if we 
wish to avoid this, the ends of cylinders should be rounded, 
and no sharp edges nor points, should be attached to the 
apparatus. 

374. The terms quantity and intensity will be under- 
stood by reference to the similar use of the same words w T ith 
respect to heat ; thus, the heat of molten iron is intense, but 
a hogshead of boiling water contains a greater quantity of 
heat than a pound of molten iron. In one case, each par- 
ticle is in very rapid vibration: in the other, very many 
particles are in vibration, and the sum of all the vibrations 
is the quantity. Electrical intensity has reference to the 
amount of force lodged in each particle. Electrical quantity 
has reference both to the number of particles affected and to 
the force lodged in each. There are both quantity and inten- 
sity in every electrified body, but the charge may be char- 
acterized by the predominance of either quality. The inten- 
sity is measured by its power to effect discharge through bad 
conductors ; thus, a long spark is evidence of great intensity. 
In statical electricity, the quantity is always small, though 
its intensity is sometimes enormous. 

Electrical Apparatus. 

375. There are many forms of electrical machines. 
Fig. 200 represents Winter's plate machine, which is one of 

Phys. 21. 



242 



ELEMENTS OF PHYSICS. 



the best. This consists of a circular plate of glass, mounted 
on a glass axis which is supported by two posts of dry 
wood and made to revolve by a winch. Friction is applied 




Fig. 200. 

to the glass plate by two rubbers, R, made of stuffed 
leather, and coated with an amalgam of mercury, tin, and 
zinc. The rubbers are kept in place by clamps attached to 
an insulated brass ball, N, called the negative conductor. 
Attached to the rubber are two wings of silk, S, to prevent 
the electricity from escaping into the air. 

The plate also passes between two wooden rings, W, which 
are attached to an insulated brass ball, P, known as the 
'prime conductor. On the side of the wooden rings, next to 
the glass plate, are two rows of brass points, which are con- 
nected by tin strips to the prime conductor. 

On turning the plate, the friction of the rubbers develops 
both electricities — the negative on the rubbers, the positive 
on the glass. The negative electricity passes to the nega- 



WINTERS MACHINE. 243 

ive conductor. The positive electricity is carried on the 
rlass between the wooden rings, and here acts by induction 
on the prime conductor, attracting its negative electricity, 
lis negative electricity collects on the points inside of the 
ings, W, and finally attains sufficient intensity to pass 
through the intervening air and unite with the positive 
electricity on the glass. The glass plate thereby becomes 
leutral as at first. The prime conductor, having given off 
negative electricity in the manner described on page 
239, remains charged with positive electricity. 

376. If both conductors were insulated, this action 
would soon cease, because the positive electricity of the 
prime conductor would act inductively on the negative of 
the other conductor, and thus only a feeble charge would be 
possible. If either conductor be uninsulated, its electric 
intensity will become zero, and thereby leave the electric 
force on the other conductor free. Hence, (1) w T hen the 
rubbers are connected by a brass chain to the ground, posi- 
tive electricity accumulates on the prime conductor. (2) 
When the brass chain connects the prime conductor to the 
ground, negative electricity accumulates on the negative 
conductor. If the hand is brought near either conductor, 
when charged, it is discharged by a spark. 

The length of the spark is wonderfully increased by the 
addition of a large wooden ring, I. An iron wire forms 
the core of this ring, and is connected with the prime con- 
ductor. Without the ring, which may be removed at the 
pleasure of the operator, the machine will give a spark two 
inches in length ; with the ring, sparks may be obtained six 
or seven times as long, but proportionally less frequent. 
The quantity of electricity is, in both cases, the same, the 
ring acting only by induction, and preventing discharge 
until electricity of high tension is attained. 



244 ELEMENTS OF PHYSICS. 

There are several varieties of the frictional machine, some 
with plates, others with cylinders, but the action of all is 
the same. 

377. There are other machines which act only by the 
induction of a charged surface. Among these are the elec- 
trophorus, and Holtz's machine, which may be briefly char- 
acterized as a revolving electrophorus. 

378. There is a limit to the accumulation of electricity 
on any surface. But, if two conducting surfaces are separ- 
ated by an insulating medium, the intensity will be in- 
creased by the mutual inducing action of the two surfaces. 
Any arrangement of this sort is said to act as a condenser. 

379. The Ley den jar is the most convenient form of the 
condenser. This consists of a glass bottle, coated both on 
the inner and outer surface with tin-foil to within three 
inches of the neck. The mouth is closed with a plug of 
varnished wood, through which passes a brass wire sur- 
mounted by a knob and 

reaching to the inner 

coating. If the jar be 

held near a machine in 

action, sparks will pass 

to the interior of the 

jar, but after awhile 

this will cease, and the 

jar is then said to be p IG . 201. 

charged. Fig. 201. 

To discharge the jar, the inner and outer coatings must 
be brought in connection. This may be done by placing 
one hand on the outer coating and bringing the other hand 
near the knob. A brilliant spark will then pass from the 
knob, and the experimenter receives a peculiar twitching 




THE LEYDEN JAR. 



24D 




sensation called the electric shock. The discharge may also 
be effected by means of a discharging rod, which consists 
of a jointed wire terminating in brass knobs. See J in 
Fig. 213. 

If the outer coating be insulated, the jar will receive little 
or no charge. But if the finger be then brought near thft 
outer coating, for every positive spark that passes into the 
jar, an equal spark of the same kind will pass from the 
outer coating to the finger. 

380. The action of the jar may be explained as follows: 
When the positive spark 
passes to the interior of 
the jar, the molecules of 
the glass become polar- 
ized, as shown in Fig. 
202. If the jar be in- fig. 202. Fig. 203. 

sulated, but little charge can be received because of the 
repulsion of the positive electricity which accumulates on 
the outer surface. If, now, the outer coating be connected 
with the ground, the positive electricity escapes from it, 
and, consequently, the outer layer becomes charged with 
negative electricity, as represented in Fig. 203. 

The outer surface is, therefore, charged by induction. 
The two surfaces have very nearly equal charges of opposite 
electricities which are held mutually bound, so that neither 
can be discharged separately. The amount of charge which 
a jar may receive is in proportion to the facility it offers for 
induction. The thinner the glass, the better; but if too 
thin, the polarization may rise high enough to cause a dis- 
charge through the glass, thereby perforating it. 

The charge is, therefore, dependent rather on the glass 
than on the coatings. This is shown by means of a jar 
with movable coatings. (Fig. 204.) If the parts be put in 



246 



ELEMENTS OF PHYSICS. 



place and the jar charged, the coatings may be removed 
and discharged. On again replacing the parts, a charge 
may be received almost as strong as if the 
coatings had not been removed. Hence, 
the principal office of the coatings is that 
of a conductor, to connect the polarized 
molecules of the glass. Another evidence 
of this is that the glass cup, B, may be 
charged separately by rotating its inner 
surface on the knob of the prime con- 
ductor, and, then, if the two coatings are 
applied, the whole combination will be dis- 
charged by a single spark. 

381. If a series of jars be insulated 
except the last, as in Fig. 205, all may be 
charged simultaneously. The electricity 
repelled from the first, charges the second, 
and so on. Each may then be discharged separately. Or 
all the similar coatings may be connected to form an elec- 




FlG. 204. 




Fig. 205. 

trical battery, as represented in Fig. 213, and discharged by 
a single spark. 

Electrical Phenomena. 



382. The laws and phenomena of electricity may be 
illustrated by a great number of experiments. 



ELECTRICAL PHENOMENA. 



247 



1. Repulsion. If a person stands on a stool supported by 
glass legs and touches the prime conductor, he becomes, in 
fact, a part of it ; and sparks may be drawn from him with 
the same effect as from the cylinder. His hair, if dry and 
loose, will stand out in a fantastic manner, because the sep- 
arate hairs are charged with the same electrical force. 

2. Attraction. If, now, a bystander bring his hand over 
the electrified person, the hairs will converge tow r ard it. 
Negative electricity is induced in the hand, and the two 
bodies oppositely electrified attract each other. 

3. Attraction and repulsion. The electrical chimes, Fig. 
206, consist of two bells in metallic connection with the 
machine, and of a third bell, insulated by 
a silk thread from the machine, but con- 
nected with the ground. Between the 
bells are small brass balls suspended by 

silk threads. On work- 
ing the machine, the 
outer bells are posi- 
tively electrified, and in- 
duce negative electricity 
in the middle bell. The 
balls are alternately at- 
tracted and repelled by FlG - 206 - 
the outer and inner bells, and thus a 
constant ringing is kept up. 

The electrical hail is exhibited by means 

of two metal plates, one connected with 

the ground and the other w T ith the ma- 

! chine, as in Fig. 207. Light pith balls 

or grotesque figures placed between the 

plates when the machine is in action rise and fall in an 

irregular manner. 





Fig. 207 



248 



ELEMENTS OF PHYSICS. 




383. The kinds of electrical discharge are three: 
(1) conductive, as when the electricity passes through a good 
conductor without light ; (2) disruptive, as effected through 
a bad conductor and attended with light; (3) convective, 
which is effected by particles of matter passing away from 
a charged surface. 

The electrical hail is an example of 
convective discharge, but usually it is 
effected by the movements of parti- 
cles of air passing away from a point 
on a charged surface. Quite a cur- 
rent of air may be detected by per- 
sons standing near such a point. 
The face feels as if a cobweb were 
drawn over it. The electric whirl 
consists of a number of such points 
suspended on a pivot. Fig. 208. i 

The reaction of the current of air is sufficient to turn the 
wheel rapidly about. 

384. Flames act as points. If a candle be held near 
a charged conductor, the flame will be repelled, as shown 

in Fig. 209, and sometimes 
extinguished. If the can- 
dle be placed on the con- 
ductor and a point turned 
toward it, the flame will 
be driven in the con- 
trary direction. This is 
due to the current of air 
which sets out from the 
point which has become 
negatively electrified by induction. 

385. Luminous effects. If a discharge be passed through 





Fig. 209. 



LUMINOUS EFFECTS. 



249 



an interrupted conductor, a succession of sparks will be ob- 
tained, which, when exhibited in a darkened room, yield a 
brilliant display. The luminous tube may be used for this 

purpose. Fig. 210. It con- 
sists of a glass tube on which 

are pasted in a spiral form 

bits of tin-foil. 
When the discharge passes 

off from the thin edge of a 

plate, a number of feeble 

sparks are obtained, which 

assume the form of a brush. 
If the discharge is effected 

in rarefied gases the effect is 

very beautiful. For this ex- 
periment a receiver called the 

aurora tube is used. Fig. 

211. In rarefied air the 

light has a bluish color; in 

nitrogen, more of a purple ; 
Fig. 210. i n hydrogen, a fine crimson. 
386. The duration of the spark is less than one -mil- 
lionth part of a second. If Newton's w T heel, Fig. 166, be 
set in very rapid rotation in a dark room and be illumi- 
nated by an electric spark, the wheel will appear stationary. 
387. The velocity of the discharge in copper wire is 
estimated at 288,000 miles in a second. This was measured 
by transmitting the discharge of a Leyden jar through a 
very long copper wire. The circuit was broken at three 
points, one at the middle of the wire and one near each 
coating. In this way three sparks were formed, which, to 
the eye, seemed instantaneous. When they were viewed by 
means of a revolving mirror, they presented the appearance 




250 



ELEMENTS OF PHYSICS. 



of three ares of equal length, the middle one rather behind 
the others, as in Fig. 212. The velocity with which the 
mirror revolved was known, and from this the retardation 
was calculated which gave the velocity of trans- 
mission. The velocity is found to vary both 
with the nature of the conducting medium and 
the intensity of the charge. 



Fig. 212. 



388. Calorific effects. Any combustible substance, as 
ether, is readily inflamed by the spark. Very thin wires 
may be melted by a discharge from a Leyden battery. Fig. 
213. Those wires are heated most, which are the worst 
conductors. In using this battery the apparatus, C7, on the 




Fig. 213. 

right of the figure, is convenient. It consists of three glass 
posts, two of which carry jointed rods, while the center 
bears on its top a glass plate. A thin gold wire, a 6, sup- 
ported on this by a paper card, c, is instantly volatilized by 
a powerful discharge. 

Chemical effects. The peculiar odor which always accom- 
panies the electrical discharge is due to the formation of 
ozone, an allotropic modification of the oxygen of the air. 




ATMOSPHERIC ELECTRICITY. 251 

A succession of sparks passed through ammonia decomposes 
it. The spark may also effect chemical combination. 

Thus, if two volumes of hydrogen and one of oxygen be 
mixed in the electrical pistol, Fig. 214, a 
single spark will cause them to combine 
with a loud explosion. 

389. The mechanical effects are shown 
when a discharge passes through a poor 
conductor. If a discharge is passed through 
a card of thick paper, a burr will be pro- 
duced in both directions. A glass plate 
may be perforated by a moderately strong FlG " 2U ' 
charge. The mechanical effects of lightning are well known. 
It rends and tears every obstacle which hinders its free 
transmission, with amazing force. The noise which accom- 
panies the spark is due to the sudden expansion of the 
surrounding air, followed by a sudden collapse, thereby pro- 
ducing a sonorous wave of condensation and rarefaction. 

390. Physiological effects. Quite a number of persons 
may receive the electric spark simultaneously. For this 
purpose, all must join hands, the first touching the knob of 
a Leyden jar, and the last the outside. 

Electricity has also been found of service in the treatment 
of some diseases. For this purpose, as well as for producing 
chemical decomposition and magnetic effects, which require 
quantity rather than intensity, some form of dynamical elec- 
tricity is generally employed. 

Atmospheric Electricity. 

Franklin demonstrated, in 1752, that a flash of lightning 
is simply an enormous spark of electricity. He raised a silk 
kite at the approach of a storm, and as soon as the rain 
had wetted his hempen kite string, thereby rendering it a 



252 ELEMENTS OF PHYSICS. 

good conductor, he succeeded in drawing sparks from a 
key hung on the string and in charging a Leyden jar. 

391. The principal source of atmospheric electricity is 
supposed to be the evaporation and subsequent condensation 
of water. A cloud becomes positively electrified by the 
accumulation of the electricity which, before its formation, 
was disseminated through its particles. It is probable that 
negative clouds are mostly due to the inductive action of 
other positively charged clouds. 

The earth beneath a cloud is subject to the same inductive 
action and becomes, by consequence, charged with electric- 
ity opposite to that of the cloud. 

392. A flash of lightning is produced when the air 
between two adjacent bodies oppositely charged becomes 
highly polarized. The light is due to the intense heat of 
the discharge which renders the particles of the air incan- 
descent. The thunder is due to the violent commotion pro- 
duced in the air by its sudden expansion along the path of 
the flash, and is prolonged by echoes. 

Heat lightning is the name applied to bright flashes of 
light observed in the horizon on summer evenings. This is 
generally due to the reflection by the atmosphere of ordi- 
nary lightning so distant that the thunder is inaudible. 

393. Lightning conductors are metallic rods used to 
protect buildings from the effects of lightning. (1.) They 
offer to the discharge the line of smallest resistance. Hence, 
the rod should be a good conductor, continuous from top to 
bottom, and should terminate in earth which is permanently 
moist. (2.) They may prevent the discharge. If the rods 
are tipped with points, the discharge may be effected silently 
and the polarization of the air particles never rise high 
enough to produce the flash. 



AURORA BOREALIS. 253 

394. There are other phenomena of atmospheric elec- 
tricity among which may be mentioned the Aurora Borealis, 
or northern lights, and St. Elmo's fire. It has been noticed 
that during the auroras the telegraph lines have been dis- 
turbed so as to prevent sending intelligible dispatches, and, 
also, that telegraphs may be worked without the aid of a 
battery when the auroras are very bright, as was the case 
in 1869. 

Recapitulation. 

I. The phenomena of statical electricity are : 
By friction. 



By other molecular disturbances. 

2. Attraction of bodies charged with unlike electricities. 

3. Repulsion of bodies charged with like electricities. 

I ^ n * ne surtace °f insulated conductors. 
1 Accumulated at pointed extremities. 

f Readily in conductors. 
By conduction < _,_ _ . . . , 

I Slowly in insulators. 

5. Transference / By convection in moving particles. 



-r. -,. .- f Spark. 

By disruption ( ^^ 



6. Induction . . By a charged body on insulating matter. 

II. The effects of statical electricity are : 

1. Mechanical . By producing fracture. 

2. Luminous . In the electric spark. 

3. Calorific . . By evolving heat. 

f By effecting combination. 

4. Chemical . ] ' ' J & . , 

( By decomposing compounds. 

5. Physiological . In producing electric shocks. 



254 



ELEMENTS OF PHYSICS. 



Dynamical Electricity. 



395. All chemical actions are attended with the devel- 
opment of electrical force. This force is identical with that 
produced by friction ; but because its discharge is continu- 
ous that department of electrical science which treats of 
electricity produced by chemical action is called dynamical 
electricity. It is also called Galvanism and Voltaic electricity 
in honor of Galvani and Volta, who were among the first 
to study its phenomena. 

The fundamental phenomena of dynamical electricity may 
be exhibited by means of the simple 
Voltaic element. Fig. 215. This usu- 
ally consists of a glass vessel contain- 
ing a plate of amalgamated * zinc and 
a plate of copper, partially immersed 
in water to which a little sulphuric 
acid has been added. A chemical 
action takes place, by which (1) the 
water is decomposed ; its hydrogen is 
liberated and its oxygen combines with the zinc to form 
zinc oxide. With water alone this action is very feeble, 
because the zinc oxide soon forms a coating on the zinc 
plate, which does not dissolve in water. (2) The sulphuric 
acid prevents the formation of this coating. This it does 
by uniting with the oxide to form zinc sulphate, which 
readily dissolves in the liquid and leaves the plate clean. 
The copper is not chemically acted upon and serves merely 
as a conductor of the electricity. 




Fig. 215. 



*To amalgamate zinc, it is first cleaned by immersion in dilute 
sulphuric acid and then mercury is rubbed over its surface. 




Fig. 216. 



ELECTRICAL CIRCUIT. 255 

As soon as the plates are immersed, there is a slight dis- 
engagement of hydrogen and both plates become feebly 
charged with electricity. If the plates are kept from 
touching, no further action will be perceived. The whole 
arrangement is in a polarized condition, which may be re- 
presented by Fig. 216, in which the positive molecules are 
shaded. The outer end of the zinc is nega- 
tive, and the portion in contact with the liquid 
is positive. The negative molecules of the 
liquid are turned toward the zinc and the pos- 
itive toward the copper plate. The copper 
thus becomes polarized in a sense opposite to that of the 
zinc. 

If, now, the plates are brought in contact either directly 
or by means of a metallic wire, a discharge will take place 
through the whole combination or circuit At the same time, 
the chemical action increases and gives rise to a series of 
charges and discharges in such rapid succession, that the dis- 
charge appears continuous and the circuit is said to be trav- 
ersed by an electrical current. The current continues so long 
as the contact is maintained, but ceases w T hen the plates are 
disconnected. The operation of connecting the plates is 
called closing the circuit, and the separating of them is called 
breaking the circuit. 

396. It is to be noted that when the circuit is closed, 
the hydrogen rises only from the surface of the copper. In 
explanation of this, it is supposed that when the oxygen 
and zinc combine, a molecule of hydrogen is set free, and 
unites with the oppositely electrified oxygen in the neigh- 
boring molecule of water, and displaces its hydrogen. This 
molecule of hydrogen is transferred to the adjacent molecule 
of water, and, in like manner, the same transference takes 
place throughout the whole series until the hydrogen of the 



256 ELEMENTS OF PHYSICS. 

molecule of water next to the copper is displaced. This 
hydrogen can not combine with the copper, but discharges 
its free positive electricity into it and escapes in a gaseous 
state. 

Each successive transfer of the hydrogen may be assumed 
to be accompanied by a separation and recombination of the 
opposite electricities. The current itself must be considered 
as due to a constant series of polarization and discharge 
among all the molecules of the Voltaic element, both liquid 
and solid, by reason of which there is a transmission of both 
electrical forces throughout the circuit, the positive going 
one way and the negative the other. 

To avoid confusion, only the direction of the positive cur- 
rent is usually given in speaking of the current. The direc- 
tion of the positive current (1) within the liquid is from 
the zinc to the copper, and (2) without the liquid, from the 
copper to the zinc. 

397. The current always sets out from the metal most 
easily acted upon by the liquid, which is therefore called 
the generating or positive plate. The other metal is called the 
conducting or negative plate. In most Voltaic elements, the 
liquid used is dilute sulphuric acid; that is, acid to w T hich 
has been added from ten to twenty times its bulk of water. 
The electric deportment of several substances with reference 
to this acid is given in the following Electro-motive series: 

-f- Zinc. Lead. Iron. Nickel. Bismuth. Antimony. 
Copper. Silver. Platinum — . 

In this list, the metals named are positive with reference 
to those that follow them, and are negative with reference 
to those that precede. 

Poles. The current passes without the liquid, from the 
negative plate back to the positive plate ; hence, if the con- 
necting wire be cut, the positive electricity will tend to 



ELECTRO -MOTIVE FORCE. 25? 

accumulate at the end of the wire attached to the negative 
or copper plate and the negative electricity to the positive 
or zinc plate. These ends are called the poles or electrodes 
of the circuit. In most combinations, zinc is used for the 
positive plate ; the wire attached to it is called the negative 
pole or electrode. The wire attached to the negative plate 
is the positive electrode or pole. 

398. The electro-motive force, or that which causes or 
tends to cause a transfer of electricity, is dependent on the 
relation which the metals bear to the liquid. It is greater 
the farther apart the metals are in the series. Dilute sul- 
phuric acid acts upon copper when taken by itself; hence, 
it tends to produce on the copper plate a current acting con- 
trary to that developed on the zinc. The electro-motive 
force of the Voltaic element is, therefore, due to the differ- 
ence of these two opposing forces. Now, as dilute sulphuric 
acid does not act upon platinum at all, a stronger current 
may be established between zinc and platinum than between 
any other two metals in the series. 

399. The quantity of electricity produced by a Voltaic 
element is proportional to the chemical activity. The work 
which the current can do is, therefore, proportional to the 
amount of zinc consumed in a given time. The quantity is 
at all times enormous. It has been calculated that an ele- 
ment which might be contained in a lady's thimble is capa- 
ble of evolving a greater quantity of electricity than the 
largest electrical machine ever constructed. 

400. The intensity of the current depends both on the 
electro-motive force and the resistance which is to be over- 
come. The greater the electro-motive force, the greater will 
be the intensity ; the greater the resistance, the less will be 
the intensity. This relation, then, may be expressed by 
Ohm's law : 

Phys. 22. 



258 



ELEMENTS OF PHYSICS. 



Intensity of current = 



Electro-motive force 
resistance. 



Solids. 




Silver 


. 100. 


Copper 


99.9 


Zinc . 


29. 


Platinum 


18. 


Iron . 


16.8 


Carbon 


.0 



401. The resistance is inversely as the conducting power 
of the substance through which the current passes. The 
conducting power of different substances of equal dimensions 
is shown relatively by the following table : 

Liquids. 

Mercury 1.6 

Dilute sulphuric acid . . .00009907 
Strong nitric acid . . . .00008868 
Common salt, saturated solution .00003152 
Sulphate of copper " " .00000542 
.04 Distilled water 00000001 

It is manifest that the resistance will increase with the 
length of the conductor, and also that it will decrease as 
the area of its cross section increases. Hence, the shorter 
and thicker the connecting wire, the less will be the resist- 
ance. So, also, the nearer the plates are together and the 
larger their area, the less will be the resistance offered to 
the current by the liquid layer between them. 

The table shows that the resistances offered by liquids are 
enormous when compared with solids. Hence, the resistance 
caused by the liquid between the plates is far greater than 
in a short conducting wire. When the conducting wires 
are very long, as in telegraphs, the external resistance may 
exceed the internal. 

402. A Voltaic Battery consists of several Voltaic ele- 




FiG. 217. 

ments so connected that the current has the same direction 
in all. The efficiency of the battery will vary with the 



VOLTAIC CIRCUIT. 259 

manner of grouping the elements. For the sake of illus- 
tration, take six elements, each containing a square inch of 
zinc, separated from a copper plate by a liquid layer an 
inch in thickness. If all the similar plates are connected, 
as represented in Fig. 217, the effect will be the same as 
that of a single element having a zinc plate of six square 
inches, one inch distant from the copper plate. Either 
arrangement is called a simple Voltaic circuit. 

In the compound Voltaic circuit the positive plate of each 




Fig. 218. 

element is connected with the negative plate of the adjoin- 
ing element, as shown in Fig. 218. 

The simple circuit is sometimes called #a quantity battery. 
It is used when the external resistance is very small. It is 
adapted for producing thermal effects, such as melting wires. 
The compound circuit is sometimes called an intensity bat- 
tery. It is used when the external resistance is very great. 
It is adapted for telegraphs, for the electric light, and for 
producing chemical decomposition. 

403. Numerous batteries have been constructed on the 
principle of the Voltaic element already described, but most 
of them have gone out of use, because of the rapid enfee- 
blement of the current. 

This may occur (1) from the gradual consumption of the 
acid and the zinc, and (2) from local action. By local action 
is meant the production of small closed circuits on the posi- 
tive plate, which are due to impurities on the zinc plate. 
This is remedied by amalgamating the zinc. (3) Besides 
these defects, the older batteries were liable to what is called 
\ the galvanic polarization of the plate. In the action of the 



260 



ELEMENTS OF PHYSICS. 



simple element, the hydrogen is apparently evolved from the 
copper. In the process of time, the copper becomes coated 
with a layer of positive hydrogen, which, of itself, would 
weaken the current, but which acts the more injuriously 
because it reduces the zinc sulphate, and thereby forms a 
layer of metallic zinc on the copper. 

404. Constant batteries obviate this last defect by pre- 
venting the permanent deposition of the hydrogen on the neg- 
ative plate. There are over fifty forms of constant batteries ; 
among the best of them are the following two-fluid batteries : 

Grove's battery consists of (1) a glass cup containing 
a hollow cylindrical zinc plate and weak sulphuric acid; 
(2) of a porous cup made of unglazed 
earthenware, containing strong nitric acid 
and a strip of platinum. The porous cup 
and its contents are placed inside the 
zinc cylinder. Fig. 219. 

The hydrogen which is liberated by 
the action of the zinc passes by osmosis 
through the porous cup, and on meeting 
the nitric acid unites with a part of its oxygen to form 
water, and reduces the acid to nitric oxide. This oxide is 
either dissolved in the liquid or escapes 
in red fumes. 

Bunsen's battery (Fig. 220) is sim- 
ply a large Grove's battery in which 
the platinum slip is replaced by a carbon 
cylinder. The chemical action is the 
same as the preceding, but as the ele- 
ments are larger, for the same amount 
of zinc consumed, Bunsen's battery gives 
a greater quantity of electricity, but less 
intensity, than Grove's. 




Fig. 219. 




Fig. 220. 



CONSTANT BATTERIES. 261 

In this form the nitric acid is sometimes advantageously 
replaced by a mixture of one part of potassium bichromate, 
two of sulphuric acid, and ten of water. 

Daniell's battery (Fig. 224) may readily be constructed 
by the student by placing within the porous cup a zinc 
plate and dilute sulphuric acid, and in the outer vessel a 
thin roll of copper with a saturated solution of sulphate of 
copper. The hydrogen, liberated by the action of the zinc, 
enters the solution of the sulphate of copper and reduces it, 
forming (1) metallic copper, which is deposited on the neg- 
ative plate ; and (2) sulphuric acid, w T hich passes by osmosis 
into the porous cup, and replaces the acid which w T as 
neutralized by the zinc. 

Recapitulation. 

I. A Voltaic element may consist of, 

1. Two metals and one fluid .... Voltaic. 

C Grove's. 

2. Two metals and two fluids . . . \ Bunsen's. 

(. Daniell's. 

II. The Voltaic current is due, 

1. To the polarization of the metallic and liquid particles, 
composing the circuit. 

2. To the contact of two dissimilar metals. 

3. To a chemical action on one metal. 

4. To a transfer of the fluid molecules. 

III. The Voltaic current depends, 

1. On the electro-motive force. 

2. On the chemical action. 

3. On the resistance, both internal and external. 



IV. The Voltaic circuit may be . . . \ 



Simple. 
Compound. 



262 



ELEMENTS OF PHYSICS. 



The Phenomena of Dynamical Electricity. 



405. The effects of the current are manifested either 
(1) within its path, or (2) external to its path. The for- 
mer will be first considered. 

Physiological effects. The science of dynamical electric- 
ity is said to owe its origin to an experiment of Galvani in 
1790, which may be repeated in the following manner: 

Let a strip of zinc be passed below the crural nerve of a 
frog, recently killed, and a 
copper wire be made to 
touch the muscles of the 
legs, as shown in Fig. 221. 
Each time the ends of the 
metals are brought together 
at A, the legs are thrown 
out in the direction of 
the dotted lines. The same 
convulsive movements take 
place when one pole of a 
battery touches the nerve 
and the other the muscles. 
The muscles contract as f ig . 221. 

often as the circuit is opened and closed, but remain quiet 
when the current is passing. Hence, the more frequently 
and abruptly the circuit is broken and closed, the greater 
will be the physiological effect. 

If the electrodes of a strong compound circuit be grasped 
with the hands, previously moistened, a shock will be expe- 
rienced; but, unless the number of elements is considerable, 
the sensation is hardly perceptible. The nerves of the pal- 
ate and of sight are easily affected. If a strip of zinc be 




EFFECTS OF THE CURRENT. 



263 



placed above the tongue and a strip of silver between the 
gums and the cheek, as often as the metals are made to 
touch, a peculiar taste will be experienced, and a flash of 
light will seem to pass before the eye. 

406. Calorific effects. If a current be passed through a 
thin metallic wire, the wire will be heated in proportion to 
the quantity of electricity and the resistance offered by the 
wire. The wire may become incandescent, may fuse, or 
even be dissipated in vapor. With the same current, the 
worst conductors will be the most readily heated. Thus, if 
a suitable current be passed through a chain made of alter- 
nate links of platinum and silver, it may 
render the platinum incandescent, while 
the silver remains dark. 

On the same principle, if a platinum 
wire be interposed in any part of the cir- 
cuit, it may be made to ignite gunpowder. 
This has been turned to account in blast- 
ing rocks and exploding torpedoes. 

407. Luminous effects. No spark is ob- 
tained unless the poles are brought in con- 
tact, or nearly so. With a moderately 
strong battery, sparks may be obtained at 
the moment the circuit is broken and 
closed. A most brilliant electric light is ^lj||||j] 
obtained by connecting the terminal wires Fig, 222. 
with carbon points, as shown in Fig. 222. The carbon points 
are first brought in contact, and the heat developed is such 
as to rentier their ends incandescent. They may then be re- 
moved to a short distance without interrupting the current, 
which forces its way through the air and produces a lumi- 
nous arc of great intensity. With 48 Bunsen's elements, the 
arc is about one-fourth of an inch long. The light is of 




264 ELEMENTS OF PHYSICS. 

far greater intensity than that obtained by the oxyhydro 
gen blow-pipe, being equal to that of 572 wax candles. 
With 600 elements, the arc is nearly eight inches long, and 
may be said to rival the brilliancy of the sun. 

The light is not due to combustion, but to the transfer- 
ence of the intensely heated particles of carbon from the 
positive to the negative electrode. In consequence of this, 
the positive electrode gradually wears away and the negative 
electrode receives a deposit. The effect of this is to increase 
the distance between the electrodes ; and, hence, some ar- 
rangement is necessary to bring them together in proportion 
as the distance alters. This may be done by the hand, or 
more conveniently by clock-work. 

The electric light is admirably adapted for illumination in 
theaters and lecture-rooms, but is not well adapted for gen- 
eral purposes of illumination. Besides the cost of its pro- 
duction and the skill required in its management, the very 
intensity of the light is a source of difficulty, as it acts inju- 
riously on the eye and throws shadows into too strong relief. 

The most refractory substances, as platinum, quartz, and 
lime, w T hen introduced into the arc are fused. The color of 
the light varies with the substances placed between the 
terminals. Gold emits a bluish light ; silver, an emerald- 
green ; lead, a purple, etc. 

408. Chemical effects. If a chemical compound, in a 
liquid state, be made to form a part of the external voltaic 
circuit, a series of decompositions will take place like those 
already described as occurring within the simple voltaic 
element. This process is called electrolysis. 

Fig. 223 represents a convenient apparatus to show the 
decomposition of water. It consists of a glass vessel, through 
the bottom of which are passed two wires terminating in 
platinum electrodes. The vessel being filled with acidulated 



ELECTROLYSIS, 



265 



water, two glass tubes also filled with water are inverted 
over the electrodes, and the outer wires are connected with 
a battery. Five of Grove's elements will cause a rapid 
decomposition of the water ; bub- 
bles of gas will collect in the 
tube above each pole. Hydro- 
gen rises from the negative pole 
and oxygen from the positive. 
The volume of the hydrogen lib- 
erated is double that of the 




oxygen. 

As the gases evolved are in 
proportion to the amount of 
zinc consumed, a modification 
of this apparatus, called a vol- 
tameter, is used to measure the 
strength of a battery. 

409. The decompositions of other compounds may 
be effected by a similar apparatus. If the electrodes are 
plunged in solutions of binary compounds, like chloride of 
copper, iodide of potassium, cyanide of silver, the metals 
collect at the negative pole and the non-metals at the posi- 
tive. On the principle that bodies dissimilarly charged 
attract each other, the metals are called electro-positive 
substances and the non-metals electro-negative. 

410. Ternary salts are also decomposed by the current, 
the metal going to the negative pole, and the acid, on the 
body which is chemically equivalent to it, going to the 
positive. 

Ordinarily, a single voltaic element will suffice for the 
decomposition of a salt. The condition in which the metal 
is deposited on the negative electrode, depends somewhat on 
the strength of the current. When the action is rapid, 



266 



ELEMENTS OF PHYSICS. 



most metals are deposited as loose, flocculent powders ; but 
if it is slow, copper, silver, gold, and some others are de- 
posited in firm, coherent layers, which exactly fit the surface 
of the electrode. 

411. Electro - metallurgy is the art of depositing the 
metals from solutions of their salts by means of the electric 
current. The solution is decomposed in the manner just 
described, and the pure metal is deposited on the negative 
electrode. This may consist of any article whatever that 




Fig. 224. 
has a conducting surface. If the material is non-conduct- 
ing, the surface may be rendered conducting by covering it 
with finely powered graphite. The positive electrode, C, 
Fig. 224, should be a plate of the same metal as that to be 
deposited — in order that the acid which is liberated may 
dissolve it, and thus maintain the strength of the solution. 
412. The processes of electro-metallurgy may be ar- 
ranged in two divisions: (1) those in which the deposit 
remains permanently fixed on the electrode, and (2) those 
in which the deposit is intended to be removed. The first 
may be represented by electroplating and the second by 
eledrotyping. 






ELECTROTYPING. 



267 



The apparatus employed in electroplating is represented 
in Fig. 224. The bath consists of a weak solution of cya- 
nide of silver. The articles to be- silvered are first carefully 
cleaned, then attached to the negative pole of the battery 
and immersed in the bath. A coating of pure silver begins 
to form at once, and may be obtained of any thickness 
desired. When the articles are first taken from the bath, 
their surfaces appear dull and white. The metallic luster 
of silver is then communicated to them by burnishing. 

By a similar process articles may be electro-gilded, or 
coated with other metals, as copper and nickel. 

413. In electrotyping, it is usual (1) to form a mold 
of the object to be copied, and then (2) to deposit within 
this a coating of some metal sufficiently thick to be stripped 
off whole. Thus, suppose we desire to copy a medal in cop- 
per. The medal is first rubbed over with graphite and the 
excess of graphite blown off; (2) an impression of the 
medal is taken in wax and the wax coated with graphite, 
as before ; (3) a copper wire is now thrust through the w T ax 
and made to connect with the layer of graphite; finally, 
(4), the wax mold is made 
the negative electrode in a 
bath of sulphate of copper. 
A tough coat of copper will 
gradually be deposited on 
the surface of the graphite, 
and, after a day or two, will 
be sufficiently thick to be 
removed. The plates from 
which this book was printed 
w T ere electrotyped in this way. - 

The student may easily copy small articles like coins and 
seals by the simple means shown in Fig. 225. A is a glass 




Fig. 225. 



268 ELEMENTS OF PHYSICS. 

vessel containing a saturated solution of sulphate of cop- 
per. B is a lamp-chimney closed below with a piece of 
bladder, and containing very dilute sulphuric acid. The 
apparatus is completed by putting a roll of amalga- 
mated zinc in the sulphuric acid, and connecting it by a 
wire to the object to be copied which is laid below the 
bladder. The connecting wire and any part of the object 
which it is not desired to copy must be carefully coated 
with wax or a resin varnish. 

Kecapitulation. 

The effects of the current within its path are: 

1. Physiological . . . Applied in some diseases. 

2. Calorific .... Applied in firing mines. 

3. Luminous .... Applied in the electric light. 

4. Chemical .... Applied in electro-metallurgy. 



Phenomena External to the Path of the Current. 

414. The voltaic current also acts inductively upon 
conductors external to its path, and thereby causes phenom- 
ena which closely ally its action to magnetism. These 
phenomena may be grouped in two divisions : 

1. Electro-magnetism considers the phenomena in which 
magnetic attraction and repulsion are caused by the voltaic 
current. 

2. Electro-dynamic induction considers the production of 
other currents in the vicinity of closed circuits. 



ELECTRO - MA GNETISM. 



269 



Conversely, permanent magnets act inductively on con- 
ducting wires, and thereby give rise to electrical currents 
without the aid of a battery. 

(3) Magneto -electricity considers the production of elec- 
trical currents by means of permanent magnets. 

Electro-Magnetism. 



415. Oersted discovered, in 1819, that a magnetic needle 
held in the vicinity of a voltaic current tends to place itself 
at right angles to the conducting wire. 




Fig. 226. 

To repeat his experiment, a magnetic needle is allowed to 
assume its natural position, pointing north and south. If, 
now, the wire conducting a voltaic current be held parallel 
to the needle, the needle will be deflected. Fig. 226. 

The direction in which the needle should turn may be 
remembered by the following rule : Suppose a diminutive 
figure of a man to be so placed in the circuit that the current 
shall enter by his feet and leave by his head: then if his face be 
turned toward the needle, its north pole will be deflected toward 
his left. 

In accordance with this rule, if the current passes above 



270 



ELEMENTS OF PHYSICS. 



the needle and goes from south to north, the north pole of 
the needle will turn toward the west. It will also turn 
westward, if the current passes below the needle from north 
to south. Hence, if the wires NS, N'S' be joined so that 
the current shall pass around the needle, the deflecting 




Fig. 227. 

power will be doubled. By coiling insulated wire many- 
times around the needle the deflecting power is so increased 
that it may be used to detect the presence of very weak 
currents, to determine their direction, and even to measure 
their intensity. An instrument constructed on this principle 
is called a galvanometer. 

The Astatic galvanometer, represented in Fig. 227, derives 
its name from the fact that it employs two magnetic 
needles fastened to the same axis of suspension, but with 



FLOATING BATTERY. 



271 



their poles reversed. The directive force of the earth on 
the needles is nearly or quite neutralized. 

416. If the conducting wire be movable, we may 

obtain results the converse of the preceding; that is, a 
straight conducting wire will tend to place itself at right 
angles to a magnet held in its vicinity. 

De La Rive's floating battery (Fig. 228) enables us to 
verify this fact. It consists of a small voltaic element which 
is floated in acidulated water by means of a 
cork. The conducting wire may be made 
straight or coiled. The spiral coil shown in 
the figure is called a helix. An elongated 
helix with its conducting wire returned 
through the axis of the coil is a solenoid. 
Fig. 229. 

417. When the current is passing 

through the wire it exhibits all the properties of a magnet. 
1. If a permanent magnet is held near the floating helix, 





Fig. 229. 



one face of the coil will be attracted by the north pole of 
the magnet and the other repelled. 

2. Each side of the helix will attract iron filings. 



272 ELEMENTS OF PHYSICS. 

3. The axis of the helix will point north and south. 

4. If two solenoids (Fig. 229) are brought near each other, 
their similar ends will repel each other ; their dissimilar ends 
will attract each other. 

5. If the conducting wire of a floating battery be straight, 
and a wire from another circuit be placed parallel to it— 
(1) The wires will be mutually attracted if the currents pass in 
the same direction, but (2) will be repelled if the currents pass in 
opposite directions. 

418. The voltaic current may also induce magnetism in 

magnetic substances. If a bar of soft iron, NS, be placed 

in the axis of a helix, the bar will „ 

be instantly magnetized on closing 

the circuit. Fig.. 230. If the helix 

is held vertically the bar will not fall 

out. If the bar be pulled down a 

little way and then let go, it will fig. 230. 

spring back to its former position. It will also attract bits 

of iron to itself, and act in every respect like a magnet. 

When the circuit is broken it loses its magnetism almost 

instantly. 

A pleasing modification of the same experiment may be 

had by passing the ends of two semicircular pieces of soft 
iron within a helix, as shown in Fig. 
231. On closing the circuit, they will 
adhere with considerable force. 





Fig. 231. 



419. Electro-magnets are bars of 
soft iron which become magnets under 
the influence of the voltaic current. Electro-magnets of 
surprising power have been made by bending bars of soft 
iron in the form of a horse-shoe, and surrounding each leg 
with many turns of insulated copper wire. Fig. 232. 



PERMANENT MAGNETS. 



273 




When a strong current is passing, the magnetism induced 
is far greater than is possible in a permanent magnet. 
Electro - magnets have been made 
that were capable of sustaining 
nearly two tons. 

Permanent magnets. When the 
current is broken, the magnetism 
ceases instantly if the iron is quite 
pure ; but, otherwise, traces of the 
magnetism will remain for some 
time. A steel bar placed in the fig. 232. 

helix (Fig. 230) will become permanently magnetized. 

420. An excellent method of making permanent mag- 
nets is shown in Fig. 233. The steel horse-shoe is applied 
to an electro-magnet and a piece of soft iron is drawn in 

the direction of the arrow 
beyond the curve, and is 
then replaced and the proc- 
ess frequently repeated. 
fig. 233. Both magnets are then 

turned over without separating them, and the other side 

treated in the same way. 

421. Various machines have been devised in the hope 
of employing the prodigious force of electro-magnets. The 
electric telegraph is by far the most important application 
of electricity. Every electric telegraph consists essentially 
of four parts : (1) a voltaic battery for generating a current; 
(2) a circuit consisting of an insulated metallic connection 
between two places ; (3) a keij, which is an instrument for 
sending signals from one station ; (4) an instrument for 
receiving signals at the other station. 

1. Any constant battery may be used for generating elec- 




274 ELEMENTS OF PHYSICS. 

tricity. In this country, some modification of DanielFs bat- 
tery is generally used. 

2. The two stations must be connected by at least one 
insulated wire. Generally this is done by passing galvanized 
iron wire over glass insulators attached to a series of tall 
wooden posts. 

At the station which sends the dispatch, the line is con- 
nected with the positive pole of the battery, but as the cur- 
rent will not pass unless the two poles of the battery are 
connected, it is also necessary to have a second conductor 
returning in the opposite direction to the negative pole of 
the battery. 

In 1837, Steinheil discovered that the earth might be 
used for the return conductor. To effect this, large metallic 
plates are buried in the ground at each station, and are 
connected at the sending station with the negative pole of 
the battery and at the receiving station with the line wire. 
The earth really dissipates the electricity, but the effect is 
the same as if it were an infinitely large return conductor 
offering an infinitely small resistance. 

422. Morse's telegraph, which is more extensively used 
than any other, requires at least two distinct parts, the signal 
key and the receiver. Beside these, a third part, called a 
relay, is necessary on long circuits as adjunct to the receiver. 
These parts are all shown in Fig. 236. If messages are to 
be received and answered, each station will require a full 
set of apparatus. 

The signal key is used for breaking and closing the circuit 
at the transmitting station. It usually consists of a brass 
lever, ad, which works on an axis, K, supported on an insu- 
lated base. The middle of the lever is always in connection 
with the line wire. At the ends are two metallic points by 
which the line wire may be brought in connection either 
with the receiver or with the positive pole of a battery. 



MORSE'S TELEGRAPH. 275 

(1) When the lever is left to itself, a spring, n, forces 
the end, a, down, so that a receiver at R (not drawn in the 
figure) is in condition to receive a dispatch from a distant 
station. (2) When a dispatch is to be sent, the end, d, is 
depressed by applying the finger to an ebonite button, /. 
The current passes from the battery up the point d, through 
the lever to K, along the wire to the receiving instrument, 
or relay, at the distant station, and thence returns by the 
earth, making the circuit complete. When the finger is 
removed, the current ceases, and hence the operator can 
close the circuit for a longer or shorter time, at his pleasure, 
by depressing or elevating the point d. 

423. The receiver, Fig. 234, consists (1) of an electro- 
magnet w T hose helices form part of the line circuit, and (2) 




Fig. 234. 

a lever which is worked by the joint action of the electro- 
magnet and an adjustable spring, S. 

One end of the coil, L, is connected with the line wire 
from the sending station, and the other, E, with the earth. 
When the circuit is closed, the electro-magnet draws down 
the armature A, which is so attached to a horizontal lever 
that when the end A is depressed, the other end, P, is 



276 ELEMENTS OF PHYSICS. 

forced up. This end carries a steel point, or style, which 
writes the signals. 

For this purpose, a narrow slip of paper is drawn by 
clock-work between the style and a revolving cylinder, and 
is indented by the pressure of the style. When the circuit 
is broken, the style is pulled down by the spring, and the 
paper is left blank. Hence, by varying the time of contact 
at the sending station, a series of signals consisting of dots 
and lines is produced at the receiving station. 

The following is the modified Morse's alphabet : 

a b c d e f g h i j 

k I mnopqrst 

u v w x 

3 4 5 



y z 


& "l 


2 


6 7 


8 9 





? 


/ 




Fig. 235. 







424. The clicking sound of the armature and the style 
indicates to the ear the same distinction of long and short 
signals that are indicated to the eye upon the paper. A 
skillful operator seldom looks at the paper when he is receiv- 
ing a message. In most cases, the paper and clock-work 
are dispensed with, and the dispatch is read only by sound. 

Tlie relay. The intensity of the current is so weakened 
after it has traversed a few miles, that the recording instru- 
ment can be worked directly by the line current only on 
short circuits. In circuits exceeding fifty miles, the actual 
receiving instrument is the relay. This is simply an electro- 
magnet whose only duty is to open and close a local circuit 
in which the recording instrument is included. 

The manner in which this is done will be rendered evi- 
dent by an inspection of Fig. 236. The line current passes 



THE BELAY. 



277 



from the positive pole of the battery, B, through the key 
and the line wire to the relay, thence around the helices of 
the relay and down to the earth plate, X. The earth con- 
nection is then said to return the current to the ground 
plate, X', and thus finally completes the circuit to the 
negative pole of the battery. 

Each time the line current passes into the relay, the 
electro-magnet attracts its armature, J., which is fixed at 
the bottom of a vertical lever, L. At the same moment, 
the upper end of the lever strikes against the screw, P. 
At this instant, a current from a local battery, B\ enters at 




Fig. 236. 

the axis of the lever, ascends to the screw, P', thence passes 
to the electro -magnet of the recording instrument, and 
finally returns to the local battery from which it started. 
When the line current ceases, the lever is drawn back by 
the spring S', and the local circuit is broken. By this 
means, the local current is made to act in unison with the 
line current, and may be used either to print a legible dis- 
patch or to transmit a fresh current to a station further on. 

425. The electrical fire-alarms, now 7 extensively used 
in large cities for indicating the localities of fires, are modi- 



278 ELEMENTS OF PHYSICS. 

fications of the Morse instrument. The properties of the 
electro-magnet have also been practically applied to various 
purposes. Among these are electric pendulums, electric 
clocks, and chronographs. The chronograph is an instru- 
ment for recording the time at which any phenomenon 
occurs. Several forms of this instrument have been devised 
which have been used to register automatically the fluctua- 
tions of barometers, thermometers, and the winds. 

426. Hitherto the attempts to use the electro-magnet 
as a motive power have not been altogether successful. 
Nevertheless, small electro-magnetic machines have been 
employed in cases where economy is of less consequence than 
convenience and facility of application, as in running sew- 
ing machines. We can not hope that they will ever be able 
to compete with steam-engines in point of economy. . 

427. There are various other forms of the telegraph, 
among which Wheatstone's needle telegraph is the most 
important. Its receiving instrument consists essentially of a 
delicate galvanometer. A modification of this instrument 
is used with the Atlantic submarine cable. 

Current Induction. 

428. The phenomena of electro - dynamic induction 
may be shown by the apparatus represented in Fig. 237. 
Let P be a helix of insulated wire through which a primary 
yurrent is passing from the battery ; and I a second helix 
connected with the galvanometer. When the primary cur- 
rent is brought near I, a secondary or induced current will be 
set up in I and will cause the deflection of the needle in 
the galvanometer. 

If the two helices are kept in the same relative position, 
the induced current soon ceases, and the needle returns to 
its old position. It will, however, be again set in motion if 



r 



CURRENT INDUCTION. 279 

the primary current is in any way changed ; that is, if the 
coil be removed, or if the current be broken or increased 
in strength. 
An induced current is, therefore, but momentary in its 




Fig. 237. 



action ; but, nevertheless, it has all the properties of the 
primary current. For instance, it may induce other cur- 




FlG. 238. 

rents on adjacent circuits, and give rise to induced currents 
of the third, fourth, and even the seventh, order. 



280 



ELEMENTS OF PHYSICS. 



429. Magneto - electrical induction is like the preced- 
ing, except that it is caused by a permanent magnet. If 
in Fig. 238 we place a bar of soft iron within the helix, 
and bring above it a strong permanent magnet instead of 
the primary coil, P, we shall obtain almost identical effects. 
The core of soft iron becomes magnetized by induction, 
and induces an electrical current in the helix, which in 
turn deflects the needle in the galvanometer. This is as 
should be expected, since we have learned that the coil, P, 
during the passage of the current, is essentially a magnet. 

430. The magneto-electrical machine is constructed 
on this principle. Fig. 239. 

This consists of a permanent magnet, A B, in front of 




which two helices of insulated copper wire are made to 
revolve on an axis, /, by means of a winch. The cores of 
the helices are made of two pieces of soft iron joined by 
an armature, tt\ The same wire is coiled about the two 
cores, but in different directions, in order that the currents 
induced by the opposite magnetic poles should be in the 



MAGNETO-ELECTRICAL MACHINES. 281 

same direction. The two ends of the wire terminate in two 
metallic plates insulated from the axis and from each other 
by ivory, and are alternately connected by the springs, S S'. 
On turning the wheel, a current of electricity is induced 
in the coil each time the core is brought before the magnet. 
It, therefore, gives rise to a rapid succession of momentary 
currents. 

431. This instrument is capable of producing sparks, 
decomposing water, igniting wires, and other effects of 
dynamical electricity. If a break piece, not shown in the 
figure, be added, an extra current of great tension will be 
produced. If the handles, PP f , be grasped with the hands 
slightly moistened, the muscles contract with such force 
that they no longer obey the will, and the handles can not 
be dropped. From its convenience, this apparatus is gener- 
ally used for applying the effects of induced currents in 
therapeutical operations. 

432. Other magneto - electrical machines constructed 
on the same principle, are in extensive use for all of the 
practical applications of electricity. The smaller are em- 
ployed in fire-alarm signals, in calling attention on tele- 
phone circuits, and other simple forms of telegraphing. 
The larger, which are frequently driven by steam-power, 
and use indifferently both permanent and electro-magnets, 
are often of remarkable power. These are in use for electro- 
plating and for the production of intense heat and light. 

Machines, which are substantially that of Fig. 239 re- 
peated several times, have been invented by Z. T. Gramme 
and by C. E. Brush, and have attracted much notice by 
reason of their compactness and efficiency. The Brush ma- 
chine is used for illuminating purposes. The inventor has 
devised a plan by w T hich he has been enabled to produce 

Phys. 24. 



282 ELEMENTS OF PHYSICS- 

economically fifty electric arcs (§ 407) of 2000 candle power 
each on the same circuit. Other inventors have endeav- 
ored to attain the same effect by rendering platinum or 
carbon incandescent, but hitherto without great success. 

433. The Telephone is an instrument used for trans- 
mitting sound-waves to a great distance. So perfect are 
some of these instruments that conversation has been car- 
ried on distinctly between stations 250 miles apart; and 
so convenient are they, that they are rapidly superseding 
short telegraphic lines, and are already in common use in 
all of the large cities. 

Two instruments are always employed: (1) the trans- 
mitter, from the sending station, applied to the mouth of 
the sender; (2) the receiver, at the distant station, ap- 
plied to the ear of the person who receives the message. 
These two instruments are connected by a wire. 

The telephone was foreshadowed in a toy known as "The 
Lovers' Telegraph." The instruments used are two hollow 
cylinders of tin. One end of each is open, and over the 
other end is stretched a piece of bladder, to serve as a 
vibrating membrane ; the two membranes are connected 
by a string fastened to the center of each. When in use 
(1) the connecting string is stretched taut; (2) the sender 
of the message speaks into the open end of his cylinder. 
He thereby excites vibrations in the tense membrane which 
correspond to waves of condensation and rarefaction pro- 
duced by his voice. (3) These vibrations are transmitted 
as sound-waves through the taut string to the membrane of 
the receiving instrument. (4) This membrane is thrown 
into vibrations exactly similar to those of the transmitting 
membrane, and (5) thereby waves of condensation and rare- 
faction, are excited in the receiving cylinder, which repro- 
duce the speech, etc., of the sender so as to render it 



THE TELEPHONE. 



283 



distinctly audible to a person whose ear is applied at the 
open end of the receiving instrument. This toy has been so 
perfected that speech can be transmitted by it over two 
miles of straight wire, and it is practically used to connect 
workshops, etc., with the sales-rooms in manufactories. 

The Bell Telephone, shown in Fig. 240, has for its 
vibrating membrane a thin iron plate, E, which is free 
to move above but not quite touching a 
permanent magnet, A. Around one end of 
the magnet is a coil of fine wire, B y which 
is connected with the binding posts, DD. 
One of the posts, D, is connected by a wire 
to the earth: the other post, by a wire to 
the distant station. The plate, E, is held 
in its place by a cup-shaped cover, to which 
the mouth is applied in sending, or the ear 
in receiving, the message. A sound made in 
front of the plate, E, produces : (1) Waves 
of condensation and rarefaction, which cause movements in 
the plate to and from the magnet, A. (2) Every such 
movement produces a disturbance in the magnetic field, 
by means of which induced currents will be set up in 
the coil (§§ 428, 429). (3) This induced current, propa- 
gated through the connecting wire, sets up vibrations in 
the plate of the receiving instrument. These vibrations 
are similar to those which caused them, and hence (4) 
excite in the air sound-waves, which reproduce the origi- 
nal sounds in pitch, quality, and even timbre, so faithfully 
that the characteristic tones of a speaker are easily recog- 
nized. No battery is used on short lines. On long lines, 
however, the sound transmitted is too feeble to be audible, 
and is, besides, liable to become confused by stronger cur- 
rents in adjacent wires. To obviate these difficulties on 




Fig. 240. 



284 ELEMENTS OF PHYSICS. 

long lines, a battery is used ; the Bell telephone is employed 
only as a receiving instrument; the transmitter resembles 
one of the two following instruments. 

434. The Microphone is an instrument capable of trans- 
mitting distinctly very feeble sounds. 

Hughes's Microphone, Fig. 241, consists essentially of 
two carbon sockets, S and $', each of which is connected 
with one of the wires in a galvanic circuit, and of a carbon 

spindle, C, placed vertically so 
as to rest in the lower socket 
and play loosely in the upper. 
Now, if while the current is pass- 
ing, a noise be made in front of 
the spindle C, it will so jar the 
spindle as to produce a greater 
or less surface contact between 
the ends of the spindle and its 
sockets. In consequence of this, the current transmitted by 
the battery will vary in like proportion. These variations 
will represent the sound-waves, and may be made to re- 
produce audible sounds if a receiving instrument such as a 
Bell's telephone be interposed in the circuit. Since the 
spindle is set in motion by very feeble . sounds, such as the 
ticking of a watch, it receives the original impulse strongly, 
and also impresses the receiving instrument strongly, and, it 
is said, that when a powerful battery is used the intensity 
of the sound is increased. 

Fig. 242 shows the interior of the Blake Transmitting Tele- 
phone, which is extensively used to send audible messages. 
It contains a diaphragm which vibrates in answer to 
the voice against a small platinum disk, which is thereby 
forced against a movable carbon cylinder, C. The disk and 
carbon are connected with a battery, and the current will 





THE PHOTOPHONE. 285 

not pass except when these are in contact. The amount of 
surface contact between them will of course vary with the 
condensation and rarefaction of the sound-waves, and conse- 
quently there will be a variation 
in the resistance of the primary 
circuit which may be reproduced 
as sound-waves in a distant tele- 
phone receiver. The receiving 
telephone is placed in connection 
with an induction coil, J, and is 
worked by the secondary current. FlG - 242 - 

Each station has a call, arranged on the principle of fire alarms. 

435. The Photophone, or Light Sounder, is the last 
invention of Mr. A. G. Bell. In this instrument sound- 
waves are made to strike upon the back of a flexible mirror, 
which is thereby thrown into vibrations. Upon the face of 
this mirror a beam of light is projected w T hich is reflected 
to a distant point in undulations which correspond to the 
vibrations of the mirror. At the distant station the re- 
flected beam is received upon a concave mirror, and by it 
concentrated upon a plate of amorphous selenium. Now, 
amorphous selenium has its conducting power for electricity 
curiously increased by exposure to light, and this property 
is utilized in the photophone. The plate of selenium is 
connected with a battery and with a telephone. By this ar- 
rangement the luminous undulations produced by the sound 
are reconverted into sounds at the distant station. Mes- 
sages have been conveyed by this instrument when the mir- 
rors w T ere 800 feet apart, and it is possible that, w T hen 
perfected, it will be of great use in military operations. 

436. Induction coils are instruments which employ both 
electric and magnetic induction. One form, in which the 
helices are separable, is shown in Fig. 243. 



286 



ELEMENTS OF PHYSICS. 



The primary coil, P, of coarse insulated copper wire, is 
connected by the screw cups -f- and — with the battery. I 
is the secondary coil of fine, insulated copper wire to which 
the handles are attached. If is a bundle of iron wires, 
which are sufficiently insulated from each other by the rust 
that soon gathers on them. The primary current is made 

M 




Fig. 243. 

to open and close by its own action. This is effected by a 
small electro-magnet, B, the spring of whose armature is 
made to open and close the circuit. 

As soon as the coil of B receives the current, the arma- 
ture is drawn down and the circuit is broken. This re- 
leases the armature, and the circuit is again closed. At 
every interruption of the primary current the iron wires 
become magnetized and demagnetized, and act inductively 
on the secondary coil. The primary current also acts in- 
ductively on the secondary coil, and by this joint action the 
intensity of the induced currents becomes much increased, 
and may even become of so high tension as to produce all 
the effects of statical electricity. 

437. RuhmkorfTs coil is made on the same principle. 
The secondary helix contains from three to thirty miles 



THERMO-ELECTRICITY. 



287 



of fine copper wire carefully insulated. With three Bunsen's 
elements and a large coil, the induced current becomes of amaz- 
ing intensity. Some of the effects of the coil are as follows: 

1. Physiological. The shocks are so violent that incautious 
experimenters have been prostrated by them. 

2. Calorific. Fine iron wires brought between the ends of 
the induced wire are melted and vaporized. 

3. Luminous. Sparks have been obtained nineteen inches 




Fig. 244. 



in length. When the discharge is passed into rarefied gases 
the phenomena of auroral light is produced in a most beau- 
tiful and varied manner. These experiments are performed 
in sealed glass tubes, known as Geisler's tubes, one of w T hich 
is shown in Fig. 244. The color of the light varies with 
the vapor inclosed in the tube, and is frequently arranged 
in bands giving the appearance of stratified light. 

4. Mechanical. Plates of glass over an inch in thickness 
may be pierced by the discharge. 

5. Leyden jars may be charged and discharged with an 
almost continuous spark of great brilliancy. 

Thermo-Electricity. 
438. If any two metals are soldered together and heated 
at their junction, an electrical current is evolved. On the 
other hand, if their junction be cooled, an electrical current 
in the opposite direction will be produced. These currents 
are called thermo-electric currents, but they differ in no 
respect from those already studied. 



288 



ELEMENTS OF PHYSICS. 



The direction of the current will depend on the metals 
which are associated together. The following thermo-electric 
series is so arranged that if any two of the substances named 
are soldered together, and heated at the soldering, the cur- 
rent will pass from the first named to that succeeding it. 



J -% % 8 



. a 

2? * 



2 2 I 

.s a i 



The most efficient electro-thermal couple is said to be 
formed of artificial sulphide of copper and metallic copper. 
Fig. 245. The usual combination is bars of antimony and 
bismuth. Fig. 246 shows a section of a thermal battery 
made up of these metals. The greater the number of pairs 
the greater will be the force of the current. Although the 
electro-motive force of a ther- ™- ^-^q 

mal battery is always low, it 
may be used to obtain the 
same results as the voltaic 
battery. 

In combining the bars, it is 
necessary to join both ends of 
all the bars except the two 

extremes. Hence, the effect of the current 
will be due to the difference of temperature 
in the two ends. This fact is utilized in the 
thermo-multiplier, shown at T in Fig. 247. 
It consists of thirty pairs of bismuth and 
antimony, inclosed in a non-conducting frame, and con- 
nected with a galvanometer which has only a few turns of 
moderately thick wire. The slightest difference in the tem- 
perature of the two ends of the thermo-multiplier will 




Fig. 245. 




A NIMA L-ELECTRICITY. 



2S9 



instantly be manifested by the deflection of the needle of 
the galvanometer. The apparatus is used in all delicate 
investigations on the subject of radiant heat. 




Fig. 247. 

Animal Electricity. 

We have already learned that electricity produces pe- 
culiar phenomena in living animals, and that one of the 
most sensitive galvanoscopes may be had in the legs of a 
recently killed frog. Matteuci has reversed this last experi- 
ment, and has succeeded in evolving a current by means of 
a battery formed of the muscles of frogs. 

439. Several species of fish have the power of giving, 
when touched, shocks like those of the Leyden jar. Among 
these are the torpedo, the gymnotus, and the silurus. Each 
of these fish has special organs for the production of elec- 
tricity. This electrical apparatus is under the control of 
the animal, and may be made to serve as a means of offense 
and defense. 

APPENDIX. 

440. The advances in Physical Science during the 
past fifty years have been marvelous. Some of its depart- 
ments, like Sound, have been greatly enlarged ; some, like 

Phys. 25. 



290 ELEMENTS OF PHYSICS. 

Heat, have been reconstructed ; some, like Electricity, are 
almost entirely of recent development. 

Among the most interesting of these advances is the 
theory which relates to the constitution of matter. Reasoning 
from the well known properties of gases — (1) their diffusion, 
which clearly necessitates motion among their molecules ; 
(2) their expansion by heat, which must also be a result 
of molecular motion ; (3) their elastic force, which increases 
with the work they have to do, another function implying 
motion — the dynamical theory of gases has been satisfac- 
torily established. 

By the terms of this theory, any gas is made up of an 
enormous number of molecules which are moving in all 
directions with great velocity. Any single molecule will 
move for a while in a free path with uniform velocity. 
When it encounters another molecule, both are brought to 
rest and then recede from each other: the direction of the 
path may be changed, but no velocity of motion is lost, be- 
cause these molecules are perfectly elastic. If the molecule 
strikes against the side of a vessel which contains it, the 
same result to the molecule follows. Thus all the mole- 
cules in an enclosed space are moving about, sometimes in 
a free path, sometimes colliding, sometimes at rest, but so 
that the total energy of the entire system remains the same. 
The average motion of any molecule will be the average of 
the entire system. Subjecting these hypotheses to a rigid 
mathematical analysis, several remarkable conclusions are 
established : 

(1) This theory of gases is in direct accord with Mario tte's 
law (Art. 172) and with all other known laws of gases; 
{2) Equal volumes of all gases, 'under like conditions, contain 
an equal number of molecules; and (3) The mass of any 
molecule and its velocity jziay be measured numerically. 



APPENDIX. 291 

Among the results attained are these : Under the normal 
pressure and temperature, a cubic centimeter of any gas 
contains (19 X 10 18 ) = 19.000,000,000,000,000,000 mole- 
cules. A hydrogen molecule has an average velocity of 
1859 meters per second; the length of its mean free path is 
965 ten billionths of a meter (-f-p^- ; its number of colli- 
sions per second, 17,750,000,000; its diametei is about 6 
ten billionths of a meter; and its mass, 46 ten million, 
million, million millionths of a gramme = 4 * . 

In a solid, the molecules have simply a vibratory motion. 
In liquids, the molecules move about, but no molecule can 
be said to have a free path. In gases the free path is many 
times the diameter of their molecule. As the density of the 
gas increases, the free path diminishes; conversely, if the 
density decreases, the length of the free path increases ; and 
in a space greatly rarefied it is several thousand times 
longer than at the normal pressure. 

441. Professor Crookes maintains that there is a fourth 
state of matter, exceedingly attenuated, which 
he calls radiant matter, and has devised a 
series of apparatus to sustain his views. 

One form is the Radiometer. Fig. 248. 
This is a small receiver nearly exhausted of 
air, having within it four light vanes black- 
ened on one side and delicately poised so as to 
revolve freely on a slender glass axis. When 
the radiometer is placed in the sunlight the 
vanes begin to revolve, and cease when re- 
moved from the light. At first he thought ^f^ ias 
that the vanes turned because of the impact of light, but 
soon it was demonstrated that the vanes moved by impact 
of the molecules which still remained in the receiver upon 
the vanes. The reason why the impact is directed upon the 




292 ELEMENTS OF PHYSICS. 

disks, is that they become slightly warmed by the heat rays 
accompanying the luminous rays ; that thereby the mole- 
cules in front of them are warmed, and, reacting from the 
glass sides of the receiver, cause the vanes to turn. The 
experiment is, in fact, a confirmation of the dynamical 
theory of gases. 

^Recapitulation. 

The science of electricity includes the phenomena of, 

1. Electricity that may be insulated . . . Statical. 

2. Electricity continually discharged in currents. Dynamical. 

Dynamical electricity investigates the phenomena, 

I. Within the path of the current : 

1. Due to chemical action .... Galvanism. 

2. Due to heat Thermo-electricity. 

3. Due to vital action Animal electricity. 

4. Due to magnetic currents .... Magnetism. 

II. External to the path of the current : 

1. Inducing magnetism in iron and steel . Electro-magnetism. 

2. Inducing currents in adjacent circuits . Electro-dynamics. 

III. Of currents induced by permanent 

magnets Magneto-electricity. 

Direct and induced currents are applied : 

1. For physiological and therapeutical purposes. 

2. For evolving intense light and heat. 

3. For effecting chemical changes. 

4. For making permanent and temporary magnets. 

5. In the Telegraph, Telephone, etc. 



6 70 *■ 



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